Question

40% of students own an iPhone, 20% of students own an Apple computer, and 16% of students own both. Let X be a Bernoulli random variable that describes “owning an iPhone”, and let Y be a Bernoulli random variable that describes “owning an Apple computer.”

(a) Determine the joint PMF of X and Y .
(b) Calculate the marginal PMFs of X and Y .

Answer 1

a)

X/Y             0                                1

0         1-(0.24+0.16+0.04) = 0.56                     0.2 - 0.16 = 0.04

1          0.4-0.16 = 0.24                                      0.16

b) P(X = 0) = 0.56 + 0.04 = 0.6

P(X = 1) = 0.24 + 0.16 = 0.4

P(Y = 0) = 0.56 + 0.24 = 0.8

P(Y = 1) = 0.04 + 0.16 = 0.2