R version 4.2.3 (2023-03-15 ucrt) -- "Shortstop Beagle"
Copyright (C) 2023 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64 (64-bit)

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> x <- rnorm(50)
> hist(x)
> hist(x,probability=TRUE)
> z <- seq(-2.5,2,0.1)
> lines(z,dnorm(z))
> z <- seq(-2.5,2.5,0.1)
> hist(x,probability=TRUE)
> lines(z,dnorm(z))
> y <- rexp(50)
> y <- rexp(50)
> hist(y,probability=TRUE)
> z2 <- seq(0,6,0.1)
> lines(z2,dexp(z2))
> plot(z2,pexp(z2))
> lines(z2,dnorm(z2),col="blue")
> 
> plot(z2,pexp(z2),type="l")
> lines(z2,dnorm(z2),col="blue")
> plot(z2,pexp(z2),type="l")
> lines(z2,dexp(z2),col="blue")
> ecdf(y)
Empirical CDF 
Call: ecdf(y)
 x[1:50] = 0.0075671, 0.015554, 0.031056,  ..., 4.2276, 4.6481
> plot(ecdf(y))
> plot(ecdf(y))
> lines(z2,pexp(z2))
> lines(z2,pexp(z2),col="red")
> lines(z2,pnorm(z2),col="blue")
> y
 [1] 0.346034943 1.779239919 4.227611918 3.302554525
 [5] 0.207280015 2.018080305 0.578814990 0.325902898
 [9] 2.537300506 1.315225562 4.648104567 0.564963880
[13] 0.816894169 0.091858808 0.204225358 0.893134940
[17] 1.322951653 0.829964187 0.247628415 1.364483530
[21] 1.852019463 0.627426800 0.160129313 0.937490303
[25] 2.187155394 0.751633704 0.690064073 0.470675648
[29] 0.015554075 0.054078710 0.031055512 0.604153465
[33] 0.934771142 3.867945483 0.508153846 1.507729555
[37] 0.135825323 0.007567149 0.418202637 0.534001115
[41] 0.174532329 0.495698506 0.810017443 1.292930607
[45] 0.872821781 0.901687504 0.057179762 0.971431497
[49] 0.099467597 0.090112556
> a <- rexp(11)
> a
 [1] 0.9704565 0.3979141 1.0000992 0.5537543
 [5] 1.3960821 0.7832498 1.9193638 0.6669857
 [9] 0.6858088 2.4391120 0.3358928
> a <- sort(a)
> quantile(a,0.5)
      50% 
0.7832498 
> a[6]
[1] 0.7832498
> quantile(a,0.3)
      30% 
0.6669857 
> a[4]
[1] 0.6669857
> quantile(a,0)
       0% 
0.3358928 
> quantile(a,1)
    100% 
2.439112 
> quantile(a,0.25)
    25% 
0.61037 
> a[3]
[1] 0.5537543
> a[4]
[1] 0.6669857
> quantile(a,seq(0,1,0.1))
       0%       10%       20%       30%       40% 
0.3358928 0.3979141 0.5537543 0.6669857 0.6858088 
      50%       60%       70%       80%       90% 
0.7832498 0.9704565 1.0000992 1.3960821 1.9193638 
     100% 
2.4391120 
> a
 [1] 0.3358928 0.3979141 0.5537543 0.6669857
 [5] 0.6858088 0.7832498 0.9704565 1.0000992
 [9] 1.3960821 1.9193638 2.4391120
> qexp(seq(0,1,0.1))
 [1] 0.0000000 0.1053605 0.2231436 0.3566749
 [5] 0.5108256 0.6931472 0.9162907 1.2039728
 [9] 1.6094379 2.3025851       Inf
> qexp(seq(0,1,0.1)) - a
 [1] -0.33589284 -0.29255359 -0.33061078 -0.31031079
 [5] -0.17498318 -0.09010267 -0.05416573  0.20387364
 [9]  0.21335582  0.38322133         Inf
> qexp(seq(0,1,0.1)) - quantile(y,seq(0,1,0.1))
          0%          10%          20%          30% 
-0.007567149  0.018541239  0.051491825  0.016679615 
         40%          50%          60%          70% 
-0.012836584  0.034401744  0.069183508  0.256300143 
         80%          90%         100% 
 0.216305178  0.080415188          Inf 
> qexp(0.3)
[1] 0.3566749
> plot(qexp(seq(0,1,0.1)),quantile(y,seq(0,1,0.1)))
> plot(qexp(seq(0,1,0.1)),
+ quantile(y,seq(0,1,0.1)),
+ ylim=c(0,1))
> plot(qexp(seq(0,1,0.1)),
+ quantile(y,seq(0,1,0.1)),
+ ylim=c(0,1),xlim=c(0,1))
> ?abline
starting httpd help server ... done
> abline(0,1) 
> plot(qexp(seq(0,1,0.05)),
+ quantile(y,seq(0,1,0.05)),
+ ylim=c(0,1),xlim=c(0,1))
> abline(0,1) 
> ?qqplot
> ?ppoints
> ppoints(11)
 [1] 0.04545455 0.13636364 0.22727273 0.31818182
 [5] 0.40909091 0.50000000 0.59090909 0.68181818
 [9] 0.77272727 0.86363636 0.95454545
> ppoints(10)
 [1] 0.06097561 0.15853659 0.25609756 0.35365854
 [5] 0.45121951 0.54878049 0.64634146 0.74390244
 [9] 0.84146341 0.93902439
> ppoints(9)
[1] 0.06756757 0.17567568 0.28378378 0.39189189
[5] 0.50000000 0.60810811 0.71621622 0.82432432
[9] 0.93243243
> ppoints(5)
[1] 0.1190476 0.3095238 0.5000000 0.6904762
[5] 0.8809524
> ppoints(4)
[1] 0.1470588 0.3823529 0.6176471 0.8529412
> ppoints(3)
[1] 0.1923077 0.5000000 0.8076923
> qqplot(y,qexp(seq(0,1,0.1)))
> abline(0,1)
> qqnorm(y)
> abline(0,1)
> qqnorm(x)
> abline(0,1)
> b <- 2*x + 2
> qqnorm(b)
> abline(0,1)
> abline(2,2,col="blue")
> qqline(b,col="red")
> x <- round(runif(30))
> y <- round(runif(30))
> z <- x + y
> x
 [1] 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1
[25] 0 0 1 0 0 0
> y
 [1] 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1
[25] 0 0 0 0 1 0
> z
 [1] 1 2 2 1 1 1 1 1 0 0 0 1 1 0 2 1 1 2 2 1 2 1 0 2
[25] 0 0 1 0 1 0
> table(x)
x
 0  1 
17 13 
> table(x,y)
   y
x   0 1
  0 9 8
  1 6 7
> df <- data.frame(x=x,y=y,z=z)
> df
   x y z
1  1 0 1
2  1 1 2
3  1 1 2
4  1 0 1
5  1 0 1
6  1 0 1
7  0 1 1
8  1 0 1
9  0 0 0
10 0 0 0
11 0 0 0
12 0 1 1
13 0 1 1
14 0 0 0
15 1 1 2
16 0 1 1
17 0 1 1
18 1 1 2
19 1 1 2
20 0 1 1
21 1 1 2
22 0 1 1
23 0 0 0
24 1 1 2
25 0 0 0
26 0 0 0
27 1 0 1
28 0 0 0
29 0 1 1
30 0 0 0
> table(x,y)
   y
x   0 1
  0 9 8
  1 6 7
> table(x,z)
   z
x   0 1 2
  0 9 8 0
  1 0 6 7
> chisq.test(x,z)

        Pearson's Chi-squared test

data:  x and z
X-squared = 16.037, df = 2, p-value =
0.0003292

Warning message:
In chisq.test(x, z) : Chi-squared approximation may be incorrect
> t <- seq(0,20,0.5)
> plot(t,dchisq(t,df=2),type="l")
> chisq.test(x,z) -> teszt
Warning message:
In chisq.test(x, z) : Chi-squared approximation may be incorrect
> teszt$stat
X-squared 
 16.03749 
> teszt$statistic
X-squared 
 16.03749 
> abline(v = teszt$stat)
> teszt$stat -> chisq
> chisq
X-squared 
 16.03749 
> pchisq(chisq)
Error in pchisq(chisq) : argument "df" is missing, with no default
> pchisq(chisq,df=2)
X-squared 
0.9996708 
> 1-pchisq(chisq,df=2)
   X-squared 
0.0003292326 
> teszt$par
df 
 2 
> teszt$parameter
df 
 2 
> teszt$p.value
[1] 0.0003292326
> qchisq(0.9,df=2)
[1] 4.60517
> abline(v = qchisq(0.9,df=2),col="red")
> chisq.test(x,y)

        Pearson's Chi-squared test with Yates' continuity
        correction

data:  x and y
X-squared = 0, df = 1, p-value = 1

> x
 [1] 1 1 1 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0 1 0 0 1 0 0 1
[28] 0 0 0
> y
 [1] 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1 1 0 1 0 0 0
[28] 0 1 0
> x <- rnorm(30)
> y <- rnorm(30) + 1
> # t-teszt: tegyuk fel, hogy Gauss valtazoink vannak
> # varhato ertek =? 0
> # H0: varhato ertek = 0
> $ H1: varhato ertek =/= 0
Error: unexpected '$' in "$"
> t.test(x)

        One Sample t-test

data:  x
t = -1.2084, df = 29, p-value = 0.2367
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.4827579  0.1241691
sample estimates:
 mean of x 
-0.1792944 

> x
 [1]  0.36599732  0.77754927 -1.17460354 -0.18660949
 [5] -0.36382404  0.22797985  0.30723704 -1.04138133
 [9]  0.39799068 -1.15321526 -0.39964973 -0.22124303
[13] -1.03517926 -0.08892231 -1.21923719 -0.53979500
[17] -0.67752702 -0.91419431 -1.60887726  0.82031848
[21]  0.05325837 -0.56113919 -0.76359421  1.19210369
[25]  0.71293663  0.03469067  2.11383701 -0.06395543
[29] -0.42868988  0.05890665
> y
 [1]  2.50467378  1.24846030  0.44549377  1.41263286
 [5]  0.83586701  1.65332882  0.64833336  1.75580450
 [9] -0.60837380  1.75898779  0.01286649  0.98887694
[13]  0.87170144  0.24049632  1.89901885  1.45670647
[17] -1.51348560  2.02528024  1.20893757  2.54278937
[21]  1.29512479  1.58135308  0.63771454 -0.50246458
[25]  2.02850849 -0.32386856  0.45529242  1.09337580
[29]  2.93888744  0.21382659
> hist(x)
> t.test(x)

        One Sample t-test

data:  x
t = -1.2084, df = 29, p-value = 0.2367
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.4827579  0.1241691
sample estimates:
 mean of x 
-0.1792944 

> teszt <- t.test(x)
> teszt$stat
        t 
-1.208377 
> var(x)
[1] 0.6604652
> mean(x)
[1] -0.1792944
> y
 [1]  2.50467378  1.24846030  0.44549377  1.41263286
 [5]  0.83586701  1.65332882  0.64833336  1.75580450
 [9] -0.60837380  1.75898779  0.01286649  0.98887694
[13]  0.87170144  0.24049632  1.89901885  1.45670647
[17] -1.51348560  2.02528024  1.20893757  2.54278937
[21]  1.29512479  1.58135308  0.63771454 -0.50246458
[25]  2.02850849 -0.32386856  0.45529242  1.09337580
[29]  2.93888744  0.21382659
> mean(y)
[1] 1.026872
> t.test(y)

        One Sample t-test

data:  y
t = 5.5505, df = 29, p-value = 5.501e-06
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 0.6484912 1.4052519
sample estimates:
mean of x 
 1.026872 

> z <- rnorm(10) + 0.1
> t.test(z)

        One Sample t-test

data:  z
t = 1.4505, df = 9, p-value = 0.1809
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.2542384  1.1629602
sample estimates:
mean of x 
0.4543609 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 1.353, df = 9, p-value = 0.2091
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.1796417  0.7143028
sample estimates:
mean of x 
0.2673305 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 0.63285, df = 9, p-value = 0.5426
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.5116183  0.9090574
sample estimates:
mean of x 
0.1987195 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 1.2571, df = 9, p-value = 0.2404
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.3633614  1.2722468
sample estimates:
mean of x 
0.4544427 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = -1.2076, df = 9, p-value = 0.258
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.9732422  0.2958049
sample estimates:
 mean of x 
-0.3387186 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = -1.6922, df = 9, p-value = 0.1249
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -1.4941164  0.2153533
sample estimates:
 mean of x 
-0.6393816 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = -0.47273, df = 9, p-value = 0.6477
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.7814750  0.5113144
sample estimates:
 mean of x 
-0.1350803 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 0.44523, df = 9, p-value = 0.6667
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.6882192  1.0255107
sample estimates:
mean of x 
0.1686457 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 0.52179, df = 9, p-value = 0.6144
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.5038254  0.8059329
sample estimates:
mean of x 
0.1510537 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 0.91726, df = 9, p-value = 0.3829
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.4457888  1.0538708
sample estimates:
mean of x 
 0.304041 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = -0.12318, df = 9, p-value = 0.9047
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.7290440  0.6537489
sample estimates:
  mean of x 
-0.03764751 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 0.10058, df = 9, p-value = 0.9221
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.6654650  0.7273959
sample estimates:
 mean of x 
0.03096547 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 0.5896, df = 9, p-value = 0.57
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.5637012  0.9611260
sample estimates:
mean of x 
0.1987124 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = -0.14721, df = 9, p-value = 0.8862
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.6128267  0.5379405
sample estimates:
  mean of x 
-0.03744309 

> z <- rnorm(10) + 0.1 ; t.test(z)

        One Sample t-test

data:  z
t = 0.48951, df = 9, p-value = 0.6362
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.5655397  0.8778829
sample estimates:
mean of x 
0.1561716 

> z <- rnorm(10) + 2 ; t.test(z)

        One Sample t-test

data:  z
t = 6.5575, df = 9, p-value = 0.0001043
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 1.553042 3.188866
sample estimates:
mean of x 
 2.370954 

> z <- rnorm(10) + 2 ; t.test(z)

        One Sample t-test

data:  z
t = 9.2795, df = 9, p-value = 6.643e-06
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 1.381191 2.271686
sample estimates:
mean of x 
 1.826438 

> z <- rnorm(10) + 2 ; t.test(z)

        One Sample t-test

data:  z
t = 4.8048, df = 9, p-value = 0.0009672
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 1.197922 3.329471
sample estimates:
mean of x 
 2.263696 

> z <- rnorm(10) + 2 ; t.test(z)

        One Sample t-test

data:  z
t = 5.736, df = 9, p-value = 0.0002812
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 1.145882 2.638270
sample estimates:
mean of x 
 1.892076 

> z <- rnorm(10); t.test(z)

        One Sample t-test

data:  z
t = 0.20735, df = 9, p-value = 0.8404
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.9593107  1.1529148
sample estimates:
 mean of x 
0.09680202 

> z <- rnorm(10); t.test(z)

        One Sample t-test

data:  z
t = -0.8245, df = 9, p-value = 0.431
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -1.1262526  0.5245671
sample estimates:
 mean of x 
-0.3008427 

> z <- rnorm(10); t.test(z)

        One Sample t-test

data:  z
t = -2.0704, df = 9, p-value = 0.06831
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.89860760  0.03976215
sample estimates:
 mean of x 
-0.4294227 

> ?t.test
> z
 [1] -0.2442521 -0.5968630 -0.4999378 -1.1152654 -1.0677565
 [6]  0.6110595 -0.0907535  0.5466837 -1.3044389 -0.5327030
> x
 [1]  0.36599732  0.77754927 -1.17460354 -0.18660949
 [5] -0.36382404  0.22797985  0.30723704 -1.04138133
 [9]  0.39799068 -1.15321526 -0.39964973 -0.22124303
[13] -1.03517926 -0.08892231 -1.21923719 -0.53979500
[17] -0.67752702 -0.91419431 -1.60887726  0.82031848
[21]  0.05325837 -0.56113919 -0.76359421  1.19210369
[25]  0.71293663  0.03469067  2.11383701 -0.06395543
[29] -0.42868988  0.05890665
> t.test(x,z)

        Welch Two Sample t-test

data:  x and z
t = 0.98084, df = 19.023, p-value = 0.339
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.2835807  0.7838374
sample estimates:
 mean of x  mean of y 
-0.1792944 -0.4294227 

> t.test(x)

        One Sample t-test

data:  x
t = -1.2084, df = 29, p-value = 0.2367
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.4827579  0.1241691
sample estimates:
 mean of x 
-0.1792944 

> t <- seq(-3,3,0.1)
> plot(t,dnorm(t))
> plot(t,dnorm(t),type="l")
> abline(v=qnorm(c(0.025,0.975)))
> t.test(x,conf.level=0.9)

        One Sample t-test

data:  x
t = -1.2084, df = 29, p-value = 0.2367
alternative hypothesis: true mean is not equal to 0
90 percent confidence interval:
 -0.43140446  0.07281568
sample estimates:
 mean of x 
-0.1792944 

> x
 [1]  0.36599732  0.77754927 -1.17460354 -0.18660949
 [5] -0.36382404  0.22797985  0.30723704 -1.04138133
 [9]  0.39799068 -1.15321526 -0.39964973 -0.22124303
[13] -1.03517926 -0.08892231 -1.21923719 -0.53979500
[17] -0.67752702 -0.91419431 -1.60887726  0.82031848
[21]  0.05325837 -0.56113919 -0.76359421  1.19210369
[25]  0.71293663  0.03469067  2.11383701 -0.06395543
[29] -0.42868988  0.05890665
> y
 [1]  2.50467378  1.24846030  0.44549377  1.41263286
 [5]  0.83586701  1.65332882  0.64833336  1.75580450
 [9] -0.60837380  1.75898779  0.01286649  0.98887694
[13]  0.87170144  0.24049632  1.89901885  1.45670647
[17] -1.51348560  2.02528024  1.20893757  2.54278937
[21]  1.29512479  1.58135308  0.63771454 -0.50246458
[25]  2.02850849 -0.32386856  0.45529242  1.09337580
[29]  2.93888744  0.21382659
> z <- x+y
> z
 [1]  2.8706711  2.0260096 -0.7291098  1.2260234  0.4720430
 [6]  1.8813087  0.9555704  0.7144232 -0.2103831  0.6057725
[11] -0.3867832  0.7676339 -0.1634778  0.1515740  0.6797817
[16]  0.9169115 -2.1910126  1.1110859 -0.3999397  3.3631078
[21]  1.3483832  1.0202139 -0.1258797  0.6896391  2.7414451
[26] -0.2891779  2.5691294  1.0294204  2.5101976  0.2727332
> y
 [1]  2.50467378  1.24846030  0.44549377  1.41263286
 [5]  0.83586701  1.65332882  0.64833336  1.75580450
 [9] -0.60837380  1.75898779  0.01286649  0.98887694
[13]  0.87170144  0.24049632  1.89901885  1.45670647
[17] -1.51348560  2.02528024  1.20893757  2.54278937
[21]  1.29512479  1.58135308  0.63771454 -0.50246458
[25]  2.02850849 -0.32386856  0.45529242  1.09337580
[29]  2.93888744  0.21382659
> v <- x + rnorm(30)
> t.test(x,v,paired=TRUE)

        Paired t-test

data:  x and v
t = 1.8855, df = 29, p-value = 0.06941
alternative hypothesis: true mean difference is not equal to 0
95 percent confidence interval:
 -0.02680605  0.65978786
sample estimates:
mean difference 
      0.3164909 

> t.test(x,alternative="greater")

        One Sample t-test

data:  x
t = -1.2084, df = 29, p-value = 0.8817
alternative hypothesis: true mean is greater than 0
95 percent confidence interval:
 -0.4314045        Inf
sample estimates:
 mean of x 
-0.1792944 

> t.test(x,alternative="less")

        One Sample t-test

data:  x
t = -1.2084, df = 29, p-value = 0.1183
alternative hypothesis: true mean is less than 0
95 percent confidence interval:
       -Inf 0.07281568
sample estimates:
 mean of x 
-0.1792944 

> t.test(x)

        One Sample t-test

data:  x
t = -1.2084, df = 29, p-value = 0.2367
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
 -0.4827579  0.1241691
sample estimates:
 mean of x 
-0.1792944 

> x
 [1]  0.36599732  0.77754927 -1.17460354 -0.18660949
 [5] -0.36382404  0.22797985  0.30723704 -1.04138133
 [9]  0.39799068 -1.15321526 -0.39964973 -0.22124303
[13] -1.03517926 -0.08892231 -1.21923719 -0.53979500
[17] -0.67752702 -0.91419431 -1.60887726  0.82031848
[21]  0.05325837 -0.56113919 -0.76359421  1.19210369
[25]  0.71293663  0.03469067  2.11383701 -0.06395543
[29] -0.42868988  0.05890665
> y
 [1]  2.50467378  1.24846030  0.44549377  1.41263286
 [5]  0.83586701  1.65332882  0.64833336  1.75580450
 [9] -0.60837380  1.75898779  0.01286649  0.98887694
[13]  0.87170144  0.24049632  1.89901885  1.45670647
[17] -1.51348560  2.02528024  1.20893757  2.54278937
[21]  1.29512479  1.58135308  0.63771454 -0.50246458
[25]  2.02850849 -0.32386856  0.45529242  1.09337580
[29]  2.93888744  0.21382659
> v
 [1] -1.00494994  1.35676207 -1.79619239  0.03434945
 [5] -0.73723705  0.68505637 -2.09348885 -1.77718721
 [9]  0.09888799 -0.71724564 -1.19926527 -1.60073374
[13]  1.03716536 -0.45613444 -2.07846129 -2.20906698
[17] -1.19872382  0.13175144 -1.95769599 -0.59719469
[21] -0.32971714 -0.10476676 -0.58964496  1.42185463
[25]  0.03027805 -0.29441528  2.88965149 -0.62558458
[29]  0.07506737 -1.26667716
> xint <- cut(x,breaks=3)
> xint
 [1] (-0.368,0.873] (-0.368,0.873] (-1.61,-0.368]
 [4] (-0.368,0.873] (-0.368,0.873] (-0.368,0.873]
 [7] (-0.368,0.873] (-1.61,-0.368] (-0.368,0.873]
[10] (-1.61,-0.368] (-1.61,-0.368] (-0.368,0.873]
[13] (-1.61,-0.368] (-0.368,0.873] (-1.61,-0.368]
[16] (-1.61,-0.368] (-1.61,-0.368] (-1.61,-0.368]
[19] (-1.61,-0.368] (-0.368,0.873] (-0.368,0.873]
[22] (-1.61,-0.368] (-1.61,-0.368] (0.873,2.12]  
[25] (-0.368,0.873] (-0.368,0.873] (0.873,2.12]  
[28] (-0.368,0.873] (-1.61,-0.368] (-0.368,0.873]
Levels: (-1.61,-0.368] (-0.368,0.873] (0.873,2.12]
> vint <- cut(v,breaks=seq(-3,3,2))
> vint
 [1] (-3,-1] (1,3]   (-3,-1] (-1,1]  (-1,1]  (-1,1] 
 [7] (-3,-1] (-3,-1] (-1,1]  (-1,1]  (-3,-1] (-3,-1]
[13] (1,3]   (-1,1]  (-3,-1] (-3,-1] (-3,-1] (-1,1] 
[19] (-3,-1] (-1,1]  (-1,1]  (-1,1]  (-1,1]  (1,3]  
[25] (-1,1]  (-1,1]  (1,3]   (-1,1]  (-1,1]  (-3,-1]
Levels: (-3,-1] (-1,1] (1,3]
> table(xint,vint)
                vint
xint             (-3,-1] (-1,1] (1,3]
  (-1.61,-0.368]       7      5     1
  (-0.368,0.873]       4     10     1
  (0.873,2.12]         0      0     2
> chisq.test(xint,vint)

        Pearson's Chi-squared test

data:  xint and vint
X-squared = 16.445, df = 4, p-value = 0.002476

Warning message:
In chisq.test(xint, vint) : Chi-squared approximation may be incorrect
> yint <- cut(y,breaks=2)
> chisq.test(xint,yint)

        Pearson's Chi-squared test

data:  xint and yint
X-squared = 3.721, df = 2, p-value = 0.1556

Warning message:
In chisq.test(xint, yint) : Chi-squared approximation may be incorrect
> table(xint,yint)
                yint
xint             (-1.52,0.713] (0.713,2.94]
  (-1.61,-0.368]             4            9
  (-0.368,0.873]             5           10
  (0.873,2.12]               2            0
>