ECSE-2500, Engineering Probability, Spring 2010, Rensselaer Polytechnic Institute

# Homework 6, due 2pm Tues Mar 30

Many of these are too hard to do by hand, and require Maple.

*(10 pts)*Let X be a normal random variable with mean=500 and variance=10,000. (This is approximately the distribution of an SAT score.) What is the probability that X>400? X>500? X>600? X>700? X>800?*(10 pts)*Let X and Y be independent normal random variables each with mean=500 and variance=10,000. What is the probability that X+Y>600? X+Y>1200?- Let X be an exponential random variable with parameter {$ \lambda=2 $}
using the definition on page 164 of the book. Maple is inconsistent with the book. .
*(2)*What is its mean?*(2)*What is its standard deviation?*(2)*What is its 2nd moment?*(2)*Verify the formula for variance in terms of the mean and 2nd moment.*(2)*Plot the pdf of X.

*(10)*Plot the pdfs of the sum of 2, 3, 4, and 5 independent exponential random variables. (They should look more and more like a normal distribution.)- The gamma random variable uses the {$ \Gamma $} function. Plot {$ \Gamma(x) $} for x from 0.5 to 5.