2. Let X denote the number Cars sold during a particular month by certain dealership. The pmf of X is I 0 1 2 3 4 5 P(X = x) .1 .2 .3 0.2 0.1 0.1 80% of all car buyers at the dealership also purchase an extended warranty. Let Y denote the number of car buyers that also buy an extended warranty. (a) Calculate the joint distribution table for X and Y. (Hint: What are values of X and Y? To calculate P(X = x,Y = y), use the fact that P(Y = y|X = x) will have a binonmial distribution with p = 0.7 and n = x. Finally calculate P(X = x, Y = y) = P(Y = y|X = x)P(X = x).) (b) Calculate the probability of the event "Every car buyer, also buys extended warranty". That is P(XY).

Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.58TI: What is the total effect on the economy of a government tax rebate of $500 to each household in...
Question
2. Let X denote the number Cars sold during a particular month by certain dealership. The pmf
of X is
I
0 1
2
3 4
5
P(X = x) .1 .2 .3 0.2 0.1 0.1
80% of all car buyers at the dealership also purchase an extended warranty. Let Y denote the
number of car buyers that also buy an extended warranty.
(a) Calculate the joint distribution table for X and Y. (Hint: What are values of X and Y?
To calculate P(X = x,Y = y), use the fact that P(Y = y|X = x) will have a binonmial
distribution with p = 0.7 and n = x. Finally calculate P(X = x, Y = y) = P(Y = y|X =
x)P(X = x).)
(b) Calculate the probability of the event "Every car buyer, also buys extended warranty".
That is P(XY).
Transcribed Image Text:2. Let X denote the number Cars sold during a particular month by certain dealership. The pmf of X is I 0 1 2 3 4 5 P(X = x) .1 .2 .3 0.2 0.1 0.1 80% of all car buyers at the dealership also purchase an extended warranty. Let Y denote the number of car buyers that also buy an extended warranty. (a) Calculate the joint distribution table for X and Y. (Hint: What are values of X and Y? To calculate P(X = x,Y = y), use the fact that P(Y = y|X = x) will have a binonmial distribution with p = 0.7 and n = x. Finally calculate P(X = x, Y = y) = P(Y = y|X = x)P(X = x).) (b) Calculate the probability of the event "Every car buyer, also buys extended warranty". That is P(XY).
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