Solution Found!
Refer to Exercise 4. Let Y denote the number of days up to
Chapter 4, Problem 5E(choose chapter or problem)
Refer to Exercise Let
denote the number of days up to and including the third day on which a red light is encountered.
a. Find \(P(Y=7)\).
b. Find \(\mu_{Y}\).
c. Find \(\sigma_{Y}^{2}\).
Equation Transcription:
Text Transcription:
P(Y=7)
mu_Y
sigma_Y^2
Questions & Answers
QUESTION:
Refer to Exercise Let
denote the number of days up to and including the third day on which a red light is encountered.
a. Find \(P(Y=7)\).
b. Find \(\mu_{Y}\).
c. Find \(\sigma_{Y}^{2}\).
Equation Transcription:
Text Transcription:
P(Y=7)
mu_Y
sigma_Y^2
ANSWER:
Answer :
Step 1 of 3:
Given, at a certain intersection of a traffic light, green is 50% of the time, yellow is 10% of the time and red is 40% of the time.
Let X = number of days that pass up to and including the first time the car encounters a red light.
Y = the number of days up to and including the third day on which a red light is encountered
Let Y follows negative Binomial distribution with n trials and k successes.
Then the probability mass function is
P( Y = n) = (1-
, for n = k, k+1, k+2,....