NOTE: please, I need the answers in typing form, not handwritten, if it will be word doc. you will help me a lot

3.36. If you take the red pill, the number of colds you get next winter will have a Poisson distribution with = 1. If you take the blue pill, the number of colds will have a Poisson distribution with = 4. Each pill is equally likely. Suppose you get three colds next winter. What is the probability you took the blue pill?

3.37. A physicist estimated that the probability of a U.S. nickel landing on its edge is one in 6000. Suppose a nickel is flipped 10,000 times. Let X be the number of times it lands on its edge. Find the probability that X is between one and three using:

(a) The exact distribution of X.

(b) An approximate distribution of X.

3.45. Simulate a Prussian soldier's death by horse kick as in Example 3.8. Create a histogram based on 10,000 repetitions. Compare to a histogram of the Poisson distribution using the command rpois(10000,0.61). (Here is exercise 3.8 below: Course hero solved before

" 3.8. There is a 50-50 chance that the queen carries the gene for hemophilia. If she is a carrier, then each prince has a 50-50 chance of having hemophilia.

(a) If the queen has had three princes without the disease, what is the probability the queen is a carrier.

(b) If there is a fourth prince, what is the probability that he will have hemophilia?"