Question

You are playing a game called cornhole and let’s assume that you are reallygood at it with the winning probability is 0.8. For the following parts, find (a) the name ofthe appropriate probability distribution and correct parameters, (b) the expected value and (c) the variance of Y.

A. Y = the number of games it takes you to lose one time.
B. Y = the number of games it takes you to lose four times.
C. Y the number of times you win out of 100 games.

Answer 1

Explanation:

Given that :

The probability of winning is 0.8

i.e P(winning) = 0.8

Then P(losing) = 0.2

a) Y ~ Geometric distribution

`P = P(loose) =0.2 \\ \\ \mu_(\delta) = (1)/(P)= (1)/(0.2)\\ \\ = 5.0 \\ \\ \\ (\sigma ^2 )/(\delta ) = (1-P)/(P^2) \\ \\ =(0.8)/(0.04) \\ \\ = 20`

b) Y ~ Negative Binomial Distribution

`P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_(\delta) = (\delta)/(P) \\ \\ =(4)/(0.2) \\ \\ = 20 \\ \\ \\ \sigma ^2_(\delta) = (\delta (1-P))/(P^2) \\ \\ = (4*0.8)/(0.04)\\ \\ = 80`

c) Y ~ Binomial Distribution;

n = 100 ; P = 0.8

`\mu_(\delta) = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_(\delta)^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16`