Math 362 Final Exam Fall ’09
1. A certain country has a careless mint. One out of every 801 coins
comes out with two heads. Pick a coin at random and flip it three
times.
a) What is the probability all three tosses are heads?
b) What is the conditional probability the coin was two-headed,
given that all three tosses were heads?
2. George decides to play roulette, betting on a single number each
time, until he wins. Since a roulette wheel has 38 slots, the prob-
ability of winning on a given play is 1
38 .
a) What is the probability he plays at least 5 times?
b) How many times should he expect to play?
c) What is the variance for the number of plays?
3. Deal 7 cards from a well-shuffled deck.
a) What is the probability at least five of the cards are spades?
b) What is the probability at least five of the cards are in the
same suit?
c) How many spades to you expect to get?
d) What is the variance for the number of spades in the hand?
4. Consider the density function
f(x, y)=15
2xy2for 0 ≤x≤1, −x≤y≤x.
0otherwise.
Compute the following:
a) f1(x)
b) E(X)
c) V(X)
d) E(Y|X)
e) V(Y|X)
f) E(Y)
g) E(Y2)
h) V(Y)
i) E(XY )
j) Cov(X, Y )
k) ρ
l) E(2X+3Y)
m) V(2X+3Y).
