Random numbers are random, you have to run aside to make the data different! ! !
1. The code is as follows:
x=runif(1000,5,10)
y=4*x-6
print(mean(x))
[1] 7.431709
print(mean(y))
[1] 23.72684
Results: The X mean is: 7.431709; the Y mean is: 23.72684;
2. The code is as follows:
print(var(x))
[1] 2.035968
print(var(y))
[1] 32.57549
c<-cov(x,y)
print©
[1] 8.143872
co<-cor(x,y)
print(co)
[1] 1
Results: D(X)=2.035968; D(Y)=32.57549; Covariance: 8.143872; Correlation coefficient: 1;
3. The code is as follows:
y1=xexp(2x^0)
print(cor(x,y1))
[1] 1
y2=xexp(2x^1)
print(cor(x,y2))
[1] 0.6717004
y3=xexp(2x^2)
print(cor(x,y3))
[1] 0.2122434
Conclusion: From the data, it can be seen that as n continues to grow, the correlation between x and yi becomes smaller and smaller. This shows that the exponential distribution is related to the uniform distribution, and if X obeys the exponential distribution, the sufficient and necessary condition is that Y=1-e^λx obeys the uniform distribution. In addition, the larger the value of x, the weaker its correlation.