Solution Found!
A traffic light at a certain intersection is green 50% of
Chapter 4, Problem 4E(choose chapter or problem)
A traffic light at a certain intersection is green of the time, yellow
of the time, and red
of the time. A car approaches this intersection once each day. Let
represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial.
a. Find \(P(X=3)\).
b. Find \(P(X \leq 3)\).
c. Find \(\mu_{X}\).
d. Find \(\sigma_{X}^{2}\).
Equation Transcription:
Text Transcription:
P(X=3)
P(X{</=}3)
mu_X
sigma_X^2
Questions & Answers
QUESTION:
A traffic light at a certain intersection is green of the time, yellow
of the time, and red
of the time. A car approaches this intersection once each day. Let
represent the number of days that pass up to and including the first time the car encounters a red light. Assume that each day represents an independent trial.
a. Find \(P(X=3)\).
b. Find \(P(X \leq 3)\).
c. Find \(\mu_{X}\).
d. Find \(\sigma_{X}^{2}\).
Equation Transcription:
Text Transcription:
P(X=3)
P(X{</=}3)
mu_X
sigma_X^2
ANSWER:
Answer:
Step 1 of 5:
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.
Assumption is that each day represents an independent trial.
Let X follows Geometric distribution and probability mass function of the Geometric distribution is
P(x) = p (1 - p , x = 1, 2, …..
Where, p = 0.40