There are 50,000 gnats, and each leaves with probability 0.037. Suppose many gnats are flying around in

Question:

There are 50,000 gnats, and each leaves with probability 0.037.
Suppose many gnats are flying around in a room. Each leaves independently with a probability that depends on the insect repellent tested. In each case:
a. Describe the random variable with a binomial giving the probability that exactly k have left.
b. Find the Poisson approximating the probability that exactly k have left and the expected number to leave.
c. Find the variance of the binomial random variable and the Poisson approximation.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...