Two questions: hypothesis test & how to win the car?

Hi guys, I really need you help me with the following two problems:

1. A drug trial gives the result that the drug works better than the placebo, with 95% confidence. What exactly does this statement mean? What further assumptions are needed to be able to deduce that the probability of the drug working is actually 95%?

2. A company has a competition to win a car. Each contestant needs to pick a positive integer. If there's at least one uinique choice, the person who made the smallest unique choice wins the car. If there are no unique choices, the company keeps the car and there is no repeat of the competition. It turns out that there are only three contestants, and you are one of them. Everyone knows before picking their numbers that there are only three contestants. How should you make your choice?

Any ideas are welcome! Many thanks.

Re: Two questions: hypothesis test & how to win the car?

Can anyone shed some light on the below:

1. Consider a set with N distinct members, and a function f defined on Q that takes the values 0, 1 such that (1/N)*Sum(over xEQ) of f(x) = p. For a subset S of Q of size n, define the sample proportion

p := p(S) = (1/N)*Sum(over xES) of f(x)

If each subset of size n is chosen with equal probability, calculate the expectation and

standard deviation of the random variable p.

2.

(a) Let X-N(0, 1) be a normally distributed random variable with mean 0 and

variance 1. Suppose that x E R, x > 0. Find upper and lower bounds for the conditional expectation

E(X | X >x)

(b) Now suppose that X has a power law distribution, P(X >x) = a*(x)^-b, for x>x0>0, and some a> 0, b> 1. Calculate the conditional expectation

E(X|X>x), x >x0

Many thanks in advance.