1. A market researcher wants to determine wheather a new model of a personal com
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Question
1. A market researcher wants to determine wheather a new model of a personal compuiter that had been advertised on a late -night talk show had achieved more brand-name recognition among people who watched the show regularly than among people who did not. After conducting a survey, it was found that 12% of all people both watched t6he show regularly and could correctly identify the product. Also, 16% of all people regularily watched the show and 41% of all people could correctly identify the product. Define a pair of random varibles as shown below. complete parts (a) through (c).
X =1 if regularly watch show X = 0 otherwise
Y = 1 if product correctly identified Y = 0 otherwise
a. Find the joint probability function of X and Y
X
Y 0 0 1
1
do not round
b. Find the conditional probability function of Y, given X =1.
P(0|1) = round to three decimal places as needed
P(1|1) = roundto three decimal places as needed.
2. A notebook computer dealer mounts a new promotional campaign. Purchasers of new computers may, if dissatisfied for any reason, return them within 2 days of purchase and receive a full refund. The cost to the dealer of such a refund is $125.The dealer estimates that 18% of all purchasers will, indeed, return computers and obtain refunds. Suppose that 70 computers are purchased during the campaign period. Complete parts a. and b. below.
a. Find the mean and the standard deviation of the number of these computers that will be returned for refunds.
The mean
(Round to one decimal place as needed.)
The standard deviation, ,
(Round to one decimal place as needed.)
b. Find the mean and standard deviation of the total refund cost that will accrue as a result of these 70 purchases.
The mean, , is $
(Round to two decimal places as needed.)
The standard deviation, is $
(Round to two decimal places as needed.)
3. If the random variables X and Y are statistically independent, then their joint cumulative distribution function can be represented as the product of the marginal cumulative distribution functions of X and Y.
True
False
Explanation / Answer
Question-1
Part-a
Joint probability distribution:
X
Y
0
1
Total
0
0.55
0.04
0.59
1
0.29
0.12
0.41
Total
0.84
0.16
1
Part-b
P(Y=0|X=1)=P(Y=0,X=1)/P(X=1)=0.04/0.16=0.250
P(Y=1|X=1)=P(Y=1,X=1)/P(X=1)=0.12/0.16=0.750
X
Y
0
1
Total
0
0.55
0.04
0.59
1
0.29
0.12
0.41
Total
0.84
0.16
1
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