Suppose X is a random variable taking on possible values 1,2,3 with respective p

Question

Suppose X is a random variable taking on possible values 1,2,3 with respective probabilites .3, .1, and .6. Y is a random variable independent from X taking on possible values 1,2,3 with respective probabilites .1, .2, and .7. Use R to determine the following.
a) Find the probability P(X + Y = 5) 1

b) Find the expected value of X. 2

c) Find the variance of X. 3

d) Find the expected value of Y. 4

e) Find the variance of Y. 5

f) Find the expected value of X*Y. (i.e. X times Y) 6

g) Find the expected value of 3X + 5Y. 7

h) Find the variance of 3X + 5Y 8

i) Copy your R script for the above into the text box here.
9

Explanation / Answer

1)

The required cases are (2,3 ) & (3,2). Hence, the probability is 0.1*0.7 + 0.6*0.2 = 0.19

2)E(x)= 1*0.3+2*0.1+3*0.6 = 2.3

3) Var(x) = 0.3 (1-2.3)^2 + 0.1(2-2.3)^2 +0.6(3-2.3)^2 = 0.81

4)E(Y) = 0.1*1+0.2*0.2+3*0.7 = 2.6

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