Question: Suppose X is a random variable taking on possible values 3,1,5 with respective probabilities .1, .3, and .6. Y is a random variable independent from

Suppose X is a random variable taking on possible values 3,1,5 with respective probabilities .1, .3, and .6. Y is a random variable independent from X taking on possible values 1,2,3 with respective probabilities .4, .3, and .3. Use R to determine the following.

a) Find the probability P(X*Y = 3)

b) Find the expected value of X.

c) Find the variance of X.

d) Find the expected value of Y.

e) Find the variance of Y.

f) Find the expected value of X*Y. (i.e. X times Y)

g) Find the expected value of 2X - 3Y.

h) Find the variance of 2X - 3Y

i) Find the expected value ofX³

i) Copy your R script for the above into the text box here.

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