Stat225Quiz 3 SolutionsA++++

STAT 225 Quiz 3

Sarah is examining the concession stands before going to watch a movie. The probability that she buys candy
is 0.70. If she buys candy, there is a 0.40 probability that she will also buy popcorn and soda, a 0.40
probability that she will buy only soda and 0.2 probability she will buy nothing else. If she does not buy
candy, she will buy popcorn and soda with probability 0.80 and 0.1 probability she buys only soda and 0.1
probability she buys nothing else. Let X represent the number of items (candy, popcorn, soda) that she
purchases.
1. Find the PMF of X. (6 points)
2. Calculate E(X). (4 points)
3. Calculate Var(X). (5 points)
P(A) = 1 􀀀 P(Ac)
P(A j B) =
P(A \ B)
P(B)
P(A) = P(A \ B) + P(A \ Bc)
P(A j B) =
P(A) P(BjA)
P(A \ B) + P(A \ Bc)
P(A \ B) = P(A) P(BjA)
E(X) =
P
x p(x)
Var(X) = E(X2) 􀀀 E(X)2
STAT 225 Quiz 3
September 20, 2013
NAME:
Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the
syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit.
Instructors will not interpret questions for you.
Sarah is examining the concession stands before going to watch a movie. The probability that she buys candy
is 0.80. If she buys candy, there is a 0.40 probability that she will also buy popcorn and soda, a 0.40
probability that she will buy only soda and 0.2 probability she will buy nothing else. If she does not buy
candy, she will buy popcorn and soda with probability 0.80 and 0.1 probability she buys only soda and 0.1
probability she buys nothing else. Let X represent the number of items (candy, popcorn, soda) that she
purchases.
1. Find the PMF of X. (6 points)
2. Calculate E(X). (4 points)
3. Calculate Var(X). (5 points)
P(A) = 1 􀀀 P(Ac)
P(A j B) =
P(A \ B)
P(B)
P(A) = P(A \ B) + P(A \ Bc)
P(A j B) =
P(A) P(BjA)
P(A \ B) + P(A \ Bc)
P(A \ B) = P(A) P(BjA)
E(X) =
P
x p(x)
Var(X) = E(X2) 􀀀 E(X)2
STAT 225 Quiz 3
September 20, 2013
NAME:
Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the
syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit.
Instructors will not interpret questions for you.
Sarah is examining the concession stands before going to watch a movie. The probability that she buys candy
is 0.75. If she buys candy, there is a 0.40 probability that she will also buy popcorn and soda, a 0.40
probability that she will buy only soda and 0.2 probability she will buy nothing else. If she does not buy
candy, she will buy popcorn and soda with probability 0.80 and 0.1 probability she buys only soda and 0.1
probability she buys nothing else. Let X represent the number of items (candy, popcorn, soda) that she
purchases.
1. Find the PMF of X. (6 points)
2. Calculate E(X). (4 points)
3. Calculate Var(X). (5 points)
P(A) = 1 􀀀 P(Ac)
P(A j B) =
P(A \ B)
P(B)
P(A) = P(A \ B) + P(A \ Bc)
P(A j B) =
P(A) P(BjA)
P(A \ B) + P(A \ Bc)
P(A \ B) = P(A) P(BjA)
E(X) =
P
x p(x)
Var(X) = E(X2) 􀀀 E(X)2
STAT 225 Quiz 3
September 20, 2013
NAME:
Directions: You have 10 minutes to complete the quiz. You are allowed a calculator as speci ed in the
syllabus. If necessary, round decimal answers to 4 signi cant digits. Show all work to receive full credit.
Instructors will not interpret questions for you.
Sarah is examining the concession stands before going to watch a movie. The probability that she buys candy
is 0.85. If she buys candy, there is a 0.40 probability that she will also buy popcorn and soda, a 0.40
probability that she will buy only soda and 0.2 probability she will buy nothing else. If she does not buy
candy, she will buy popcorn and soda with probability 0.80 and 0.1 probability she buys only soda and 0.1
probability she buys nothing else. Let X represent the number of items (candy, popcorn, soda) that she
purchases.
1. Find the PMF of X. (6 points)
2. Calculate E(X). (4 points)
3. Calculate Var(X). (5 points)
P(A) = 1 􀀀 P(Ac)
P(A j B) =
P(A \ B)
P(B)
P(A) = P(A \ B) + P(A \ Bc)
P(A j B) =
P(A) P(BjA)
P(A \ B) + P(A \ Bc)
P(A \ B) = P(A) P(BjA)
E(X) =
P
x p(x)
Var(X) = E(X2) 􀀀 E(X)2