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Let X be the number of times I flip a head on a fair coin in...

Let X be the number of times I flip a head on a fair coin in 1 minute. From this description, we know that the random variable X follows a Poisson distribution. The probability function of a Poisson distribution is

P[X = x] = e-λ λx / x!

1. What is the sample space of X? Explain how you got that answer.

2. Prove that the expected value of X is λ.

3. Given that λ = 30, what is the probability that I get 30 heads? That is, what is P[X = 30]?

4. Given that I got 30 heads in the first minute, what is the probability of getting 30 heads in the second minute?

Math   Statistics-And-Probability   
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