Question

A market researcher wants to determine whether a new model of a personal computer 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 15% of all people both watched the show regularly and could correctly identify the product. We also know that 16% of all people regularly watched the show and that 45% of all people could correctly identify the product. Define X

Answer 1

Hello you question lacks some information attached below is the missing information

answer : When X = 1 people regularly watch the show otherwise X = 0

Joint probability = 1 ( 100%)

Explanation:

16% = regularly watched the show

45% = correctly identify with the product

15% = watched the show and correctly identify the product

To define X

When X = 1 if people regularly watch the show otherwise X = 0

To define Y

When Y = if people identify correctly identify with product otherwise Y = 0

Determining the joint probability distribution of x and y

= P ( x ∩ y )

to obtain the joint probability we have to apply the marginal probabilities of X and Y

when : y = 0, x = 0, 1 marginal distribution of y = 0.54 + 0.01 = 0.55

when : y = 1 , x = 0, 1 marginal distribution of y = 0.30 + 0.15 = 0.45

when : x = 0 , y = 0,1 marginal distribution of x = 0.54 + 0.30 = 0.84

when : x = 1 , y = 0 , 1 marginal distribution of x = 0.01 + 0.15 = 0.16

as can be seen above the joint probability distribution of x and y = 1