Question

there is no given probability of commercial, just given 8 commercial, so I don't know what is given p here.

Consider probability density function(pdf) for a Binomial rnadom variable:

Thank you!

1. In a 30-minute episode of cable-television there are on average 8 commercials. Let X be the 30-minute episode of cable-television number of commercials in a C (a) When watching a half-hour show, what is the probability that you see 9 commercials? (b) You decide to binge-watch 8 episodes of Schitt's Creek. What is the probability that in 5 of the 8 episodes there are 9 commercials? P(X)f(x) P (1 P)" п-т

Answer 1

X ~ Poisson(8)

The probability mass function of X is

8 P(X x) ed -, x = 0,1,2,3, !

a) When watching a half hour show, the probability that one sees 9 commercial

P(X 9) ed 0.124077 9!

b) Let Y denotes the number of binge-watch episodes in which there are 9 commercials out of 8 episodes of Schitt's Creek.

Y ~ Binomial(n = 8, p = 0.124077)

The probability mass function of Y is

8-4 P(Y y) 0.124077 (1 0.124077), y0,1,2,., 8

Now,

The probability that in 5 of the 8 episodes there are 9 commercials

*0.1240773 (1 -0.124077) 8-5 P(Y 5) 0.0011067