Hey everyone, I'm pressed for time and I've been swamped with having to work both jobs this week that i haven't been able to go to class and get all the information i need. I was hoping someone could help me answer some of the homework questions. My textbook is pretty worthless and more confusing that anything. So help is appreciated! They should be fairly simple to anyone that is good at this subject.
1. If X is a discrete uniform random variable, that is, P(X = k) = 1/n for
k = 1, 2, . . . , n, find E[X] and V (X).
2. Suppose that two lotteries each have n possible numbers and the same payoff.
In terms of expected gain, is it better to buy two tickets from one of the lotteries
or one from each?
3. A random square has a side length that is a uniform[0,1] random variable. Find
the expected area of the square.
4. If n men throw their hats into a pile and each man takes a hat at random, what
is the expected number of matches? (Hint: Express the number of matches as
a sum of n Bernoulli random variables.)
5. Let X be uniformly distributed on the interval [1,2]. That is, X Uniform[1, 2].
Find E[1/X] and 1/E[X].
Any help on any of these questions would be appreciated!
1. If X is a discrete uniform random variable, that is, P(X = k) = 1/n for
k = 1, 2, . . . , n, find E[X] and V (X).
2. Suppose that two lotteries each have n possible numbers and the same payoff.
In terms of expected gain, is it better to buy two tickets from one of the lotteries
or one from each?
3. A random square has a side length that is a uniform[0,1] random variable. Find
the expected area of the square.
4. If n men throw their hats into a pile and each man takes a hat at random, what
is the expected number of matches? (Hint: Express the number of matches as
a sum of n Bernoulli random variables.)
5. Let X be uniformly distributed on the interval [1,2]. That is, X Uniform[1, 2].
Find E[1/X] and 1/E[X].
Any help on any of these questions would be appreciated!