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

# Homework 5, due 2pm Tues Mar 23 2010

- The player tosses a fair coin 4 times and counts the number of heads,
k. His reward, Y, is k
^{2}.*(5 pts)*Write the pmf of Y.*(5)*What is E[Y]?*(5)*What is Var[Y]?

- A transmission channel introduces an error 10% of the time. It
transmits 10 messages. Let X be the number of errors.
*(5)*What is the pmf of X?*(5)*What is the probability of 2 or fewer errors?*(5)*What is E[X]?*(5)*What is Var[X]?

- You have an unfair coin, where the probability of heads is 0.4. You toss
it 4 times. Let X be the number of heads.
*(5)*What is the probability of 2 or more heads?*(5)*What is E[X]?*(5)*What is Var[X]?

- Look at example 3.19 on page 108
*(5)*Redo it, but now with p=1/2.*(10)*Do a plot of the fraction of packets dropped as function of p, for 0<=p<=1. Use the computer tool of your choice.

- We are picking two independent random variables, X and Y, uniformly in the interval
[0,1].
*(5)*What is E[X]?*(5)*What is Var[X]?*(5)*What is E[X+Y]?*(5)*What is Var[X+Y]?*(5)*What is E[X|X>Y]?*(5)*What is Var[X|X>Y]?

- During the Perseid meteor shower, assume that meteors are independent, and
that, on average, there is one per minute. Let X be the number of
meteors in 2 minutes.
*(5)*What is the pmf of X?*(5)*What is E[X]?*(5)*What is the probability that X=0?

*(15)*Problem 3.88 on page 139.

*Total: 145*