GBUS280 Business STAT
Assignment 3B
Name:
1. (Tip: Refer to Chapter 5 Example 3 in Sakai)
Please complete the following contingency table and answer the following questions
Y=1
Y=2
PMF of X
X=1
P(X=1, Y=1) = 0.30
P(X=1, Y=2) = 0.20
P(X=1) = 0.50
X=2
P(X=2, Y=1) = 0.25
P(X=2, Y=2) = 0.25
P(X=2) = 0.50
PMF of Y
P(Y=1) = 0.55
P(Y= 2) = 0.45
1.00
a. Please complete the table
b. Are X=1 and Y=1 independent? Why (state the formula)?
P(A/B) = P(A)
P(A/B) = P(A and B)/P(B) = 0.30/0.55 = 0.545
They are not independent since the formula is not correct anymore. X=1 is 0.5 but the result is
0.545
c. Are X=1 and Y=1 mutually exclusive? Why (state the formula)?
P(A or B) = P(A) + P(B)
They are not mutually excusive since the formula would not be correct.
2. Suppose X is a binomial random variable with n=5 and π=0.40. Then X~B(5, 0.40). How
much is the probability (Please keep all the decimals) of
a. P(X = 0) (Formula please, if applicable)
1
(n!/x!(n-x)!) (p)^x(1-p)^n-x
= 0.0777
b. P(X = 1) (Formula please, if applicable)
= 0.2592
c. P(X = 2) (Formula please, if applicable)
= 0.3456
d. P(X = 3) (Formula please, if applicable)
= 0.2304
e. P(X < 2) (Formula please, if applicable)
P(X=0) + P(X=1) + P(X=2) = 0.6825
f. What is the expected value of X? (Formula please, if applicable)
P(X=4) = 0.0768, P(X=5) = 0.0102
0x0.0777 + 1x0.2592 + 2x0.3456 + 3x0.2304 + 4x0.0768 + 5x0.0102 = 1.9998
g. What is the variance of X? (Formula please, if applicable)
Variance = 5x0.4(1-0.4) = 1.2
h. What is the standard deviation of X? (Formula please, if applicable)
√1.2 = 1.095
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