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Math 130B

1. Let X = ”(0,1) andF = |X|.

(a) What is the correlation coeffecient pxy ?

(b) Are X and Y independent? Justify your answer.

2. A = Bin(n,p) and B = Bin(A, what is E[A\B = 0]

3. A game is played withe N distinct coins lined up, and the k^th coin in line has a

probability of 3~^k to flip heads (for k = 1, 2,..., TV)

A player must go down the line and flip each coin. Once any one coin has flipped heads
twice (not necessarily in a row), it can be removed. What is the expected number of total
coin flips needed to remove all coins and finish the game?

4. Let T be the triangle with verticies (0,0), (0,2) and (2,0).

.. (k(2x + y) e T

X and Y are random variables with joint density fxYX^^ y)= <

" [0 else

What is the covariance of X and Y?

5. A fair 4 sided die with sides labeled 1,2,3, and 4 is rolled repeatedly. Let X be the number of rolls required to get a 3 or 4 and Y be the number of rolls required to get a 4.

What is Var{Y\X = 1]?