Stats-Probability

Would really urgently appreciate answers to these questions. Thanks.

3. 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?
4. A random square has a side length that is a uniform[0,1] random variable. Find
the expected area of the square.
5. 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.)


Well Johnny, we (at least I) don't simply respond to requests for answers. The objective here is not just "getting the answer", but seeing that you "get the method" behind it too.
What have you tried? Where are you stuck right now?

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