STAT 341
Homework 1 Solutions
3. There are 4 4 possibilities, say (left front,right front) where the rst left element of the pair is the
response of student A and the right element is the response of student B. Of these pairs, only 4
have common elements,
STAT 341
Practice Exam 3
1. Suppose that X Poisson( = 5). Hence
F (x) =
0,
for x 0,
1 exp(x) for 0 < x.
(1)
a. Find p25 and p75 , the 25th and 75th percentiles of the distribution of X .
b. Suppose that Y = r(X ) is dened by
1, for x p25 ,
2 for p25 < x
STAT 341
Sample Exam II
1a. Given a league with 9 teams, A, B, C, . . . , I , how many games must be played in order that each
team play every other team once? C9,2 = 36
1b. How many games does team A play in? 8
1c. How many games must be played in order
STAT 341
Homework 8
1. Suppose that a random variable X can have each of seven values 3, 2, 1, 0, 1, 2, 3 with equal
probability. Determine the probability function and distribution function of the random variable
Y = X2 X.
y
0
2
6
12
P (Y = y ) 2/7 2/7 2
STAT 341
Homework 8 Solutions
34. Let F denote the probability that a person selected at random is female. Then, P (F ) = .5 = P (F c ).
Let B denote the event that a random selected person is color-blind. Then P (B |F ) = .0025 and
P (B |F c ) = .05). We
STAT 341
Homework 6 Solutions
41. Note that X Bin(1500, .002) and that X is approximately Poisson with = np = 3. Then, since
P (X = x) x e /x!, P (X = 0) e3 = 0.04979.
47. Let X denote the number of passengers that dont show up. The distribution of X is b
STAT 341
Homework 5 Solutions
25. X = # of 3s Bin(8, 1/6). Then,
P (X = 2) = C8,2
1
6
2
5
6
6
=
8!
2!6!
1
6
2
5
6
6
= .26047.
27. Let W denote the outcome of team B winning a game. Then, B will win the series if B wins the
rst 4 games, or 3 of the rst 4 g
STAT 341
Homework 4 Solutions
1. 9!
2. 4 3 5 = 60
3. P16,3 = 16 15 14
4. C30,5
5. P10,6 if order is important, and C10,6 if order is not important.
6. We need to determine the number of pairs that can be formed when the order is not important.
Hence, the
STAT 341
Homework 3 Solutions
40. P (win) = 1/6 and P (lose) = 5/6. Set W equal to the value or return of the game, and x to be the
pay-o when the game is won. Thus,
0 = EW = 1 5/6 + (x 1) 1/6.
Solving for x yields x = 6.
48. Let Y be a random variable th
STAT 341
Homework 2 Solutions
20. A and B are independent. To show, we need to compute P (A), P (B ) and P (A B ). First P (A) =
4/52. The event B = spade on the second draw will happen if we observe a spade on both the
rst and second draws, or if we obse
STAT 341
Practice Exam 3
Final: Tuesday, December 15, 8AM.
1. Suppose that X has the following distribution function
for x 0
0,
x
, for 0 < x < 2,
82
F (x) =
x , for 2 x < 4,
16
1,
for 4 x.
a. Find p25 and p75 , the 25th and 75th percentiles of the di