Question

a) Phone calls are received at Diana’s house at the rate of λ = 3 per hour. If Diana takes a 20 minute shower, what is the probability that she will receive at least one phone call during the shower. You can assume that the number of phone calls in any given time interval has a Poisson distribution

b) Let X be a random variable with E(X) = 0 and E(X2^2) = 2. Then what statement can you make about P{ |X| > 3 sqrt(2) } ? (USE CHEBYSHEV'S THEOREM)

c)c) Suppose that 55% of all registered Florida Republican voters support Marco Rubio and the rest support Patrick Murphy? Suppose we take a random sample of 100 registered Florida republican voters and count X = # who support Marco Rubio and Y = # who support Patrick Murphy. What is E(X-Y)?

Answer 1

Solution:

Questin a) We are given that: Phone calls are received at Diana’s house at the rate of per hour.

If Diana takes a 20 minute shower, what is the probability that she will receive at least one phone call during the shower.

So for 60 minutes rate of then for 20 monutes rate of

Since 60/3=20 then 3/3=1

Thus rate of

Thus using Poisson distribution:

P( At least one phone call) = ............?

Thus the probability that she will receive at least one phone call during the shower is 0.6321.