Problem A: Let X1 and X2 be independent random variables, X1 has pdf f (x) = 6x(1 – x) for 0 < x < 1, and X2 has pmff (x) = x/17 for x = 3,5,9. a) Find the mean and variance of 7X1 - 3X2. b) Find E (X{X²). Problem B: Let X, and X2 be independent random variables, X, is binomial with parameters 4 and 0.7, and X2 is binomial with parameters 5 and 0.5. a) Find P(X,X, = 8). b) Find P(X, + X2 = 8).
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You are given a fair die, i.e. the outcomes of any throw are contained in the sample space 
(a) Derive the joint pdf of X and Y. Provide this in the form of a table
Y=0 Y=1
| X=0 | ||
| X=1 |
b) What is the marginal probability distribution of Y?
(c) What is the conditional probability distribution of X, given that Y = 1?
(d) What is E (X|Y = 1)?
(e) What is Cov (X, Y )?
(f) Are X and Y independent random variables?
