Question

Write an R code that does the following:

(a) Generate n samples x from a random variable X that has a uniform density on [0,3]. Now generate samples of Y using the equation: y = α/(x + β). For starters, set α = 1, β = 1

The R code:

x=runif(n=1000, min = 0, max = 3)
x

y=1/x+1
y

Please answer the following:

b) Use plot(x,y) to check if you got the right curve.

c) How does the correlation depend on α and how can you make the correlation close to 1?

d) How can you make the correlation close to 0?

e) Can you ever make the correlation positive?

Answer 1

b) plots of the given R code is-

c) as we increase alpha

for alpha=5, beta=1

for alpha=20, beta=1

what we see, as we increase alpha the curved path increases.it is not possible to make correlation 1 since both x and y are inversely related.

d)correlation will be zero when we get a straight line parallel to x axis.

e) it is possible when alpha take negative value