Homework 4

If X and Y are RVs so that E(X) = 2, E(Y) = -1, E(X^2) = 10, E(Y^2) = 6 and Cov(X,Y) = -2, what is E(XY)?

In #1, what is Var(X+Y)?

In #1 what is the correlation of X and Y?

If you have a biased coin that is heads 65% of the time and you flip it (independently) 20 times in a row, what is the probability that you see exactly 13 heads?

What is the variance of the number of heads in #4?

A frog can hop along a straight path, jumping either 1 step forward or backward and is equally likely to jump in either direction. If he takes 7 total steps, what is the probability he ends up 1 foot forward from where he started?

What is the expected end position of the frog in #6?

The malpractice claim rate of a doctor is 0.01, i.e. 1% of patients will file a claim against the doctor. What is the probability that the next malpractice claim against the doctor will come from one of the next 70 patients she sees?

What is the expected number of patients the doctor will see before the next malpractice claim?

You are writing homework problems and know that your error rate is 4%, that is there is a 0.04 probability that a given homework problem contains an error. If you look through your problems for errors, what is the probability that the first 9 problems you check are error-free?