MA 2631 Conference 5

Original price was: $35.00.Current price is: $30.00.

Rate this product

MA 2631 Conference 5

The exponential random variable with parameter λ > 0:
f(x) = (
λe−λx x ≥ 0
0 x < 0
1. Let X be an exponential random variable with parameter λ. Calculate Var[X] in two ways:
(a) By looking up E[X] in the lecture notes, calculating E[X2
] directly using the definition of expectation, and the formula Var[X] = E[X2
] − (E[X])2
(b) By deriving the moment generating function MX(t) = E[e
tX] (a challenge problem).
2. Suppose that the length of a phone call in minutes is an exponential random variable with parameter
λ =
10 . If someone arrives immediately ahead of you at public telephone booth, find the probability
you will have to wait
(a) more than 10 minutes;
(b) not more than one standard deviation away from the mean.
3. We say that a nonnegative random variable X is memoryless if
P[X > s + t|X > t] = P[X > s] for all s, t ≥ 0.
Show that an exponential random variable X with parameter λ is memoryless.
4. Suppose that the number of miles that a car can run before its battery wears out is exponentially
distributed with an average value of 10, 000 miles. If a person desires to take a 5,000 mile trip, what
is the probability that he or she will be able to complete the trip without having to replace the car


There are no reviews yet.

Be the first to review “MA 2631 Conference 5”

Your email address will not be published. Required fields are marked *

Scroll to Top