Question

Problem 7. Suppose that a coin will be tossed repeatedly 100 times; let N be the number of Heads obtained from 100 fips of this coin. But you are not certain that the coin is a fair coin.it might be somewhat biased. That is, the probability of Heads from a single toss might not be 1/2. You decide, based on prior data, to model your uncertainty about the probability of Heads by making this probability into random variable as wl. In particular, to model the "fuzziness in our knowledge of p, assume that p is a value from a random distribution with probability density c *p * (1-p). for P ranging between 0 and 1. The constant c in the pdf is just a normalizing constant that needs to be chosen so that the total probability in the distribution is 1 a) In this model, calculate the unconditional mean and standard deviation for the b) How do the answers in Part a) compare to the answers you would get if you c) Calculate the unconditional probability mass function of N, and use the pmf d) How does the probability found in Part c) compare to the answer you would number of Heads, N just assumed that the coin was fair? to find the probability that you'll get between 40 and 60 heads. get if you just assumed that the coin was fair?

Answer 1