Help me!!! Thanks for helping me

9. Distributions. (5 parts.) 1. Recall that X ~ Poisson (1 ) could be derived as a limit of a binomial distribution Y ~ B(p,n) as n - co. For what value of p (in terms of n and A) is this true? 2. What is the distribution of the random variable corresponding to the number of trials where one flips one coin with probability of heads equal to p and another with probability of heads equal to q and one stops if either is heads? (Note each trial consists of two flips, and the variable is the number of trials. For example, if in the first trial, both coins are heads, the random variable has value 1) If you use a standard distribution, state the parameter(s), otherwise give a formula for Pr[X = i].) 3. Let m balls be placed uniformly at random into n bins. What is the expected number of bins with exactly 2 balls? (You may assume m > 2.) 4. For independent random variables X ~ Geom(p) and Y ~ Geom(p), what is the distribution of the random variable Z = X + Y