SDS321HW25Sol - SDS321HW25Sol 1 Based on US population...

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SDS321HW25Sol 1. Based on US population statistics, we can model the height of a randomly selected man using a normal random variable with mean 69.1 inches and standard deviation 2.9 inches. We can model the height of a randomly selected woman using a normal random variable with mean 63.7 inches and standard deviation 2.7 inches. a. Find the probability of a man being between 6' and 6'2" tall. F(1.68)-F(1)= 0.9545 - 0:8413 = 0.1132 b. Suppose a person was selected at random. Assume that p(male)=p(female)=.5. Given that the individual selected is shorter than 5.5, what is the probability that the person selected is a male? P ( M | X < 65) = P ( X < 65| M ) P ( M ) P ( X < 65| M ) P ( M ) + P ( X < 65| F ) P ( F ) = .0793 .0793 + .6844 = .1038 2. Suppose that you have three coins. Two are fair, with probability 0.5 of yielding heads. The third is biased, with probability 0.7 of yielding heads. You pick a coin at random, and throw it 20 times. You get 13 heads and 7 tails. Let Θ = .7 if the coin is biased, and Θ = .5 if the coin is fair. What is the posterior probability that the coin is fair, i.e. what is P( Θ = .7|X = 13)?
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