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
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 th
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
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 ra
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-b
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 p
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 th
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
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.
Solvin
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
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. Fin