Question

A class begins on time 50% of the time. The remaining 50 % of the time, the delay in the start of the class follows an exponential distribution with an expected value of 3 minutes. Write the PDF and the CDF for this distribution. What is the probability that a class starts more than 5 minutes after the start time?

Answer 1

Let X denote the delay in the start of the class (in minutes)

X will have a mixed distribution of both discrete and continuous

PDF of X is:

P(X < 0) = 0

P(X = 0) = 0.5

P(X > 0) = = , x > 0

CDF of X is:

F(x) = 0, x < 0

F(x) = 0.5 + = , x ≥ 0

Probability that a class starts more than 5 minutes after the start time

= P(X > 5) = 1 - P(X ≤ 5) = 1 - F(5)

= = 0.09444