Question

In the city of Akronage a traditional baseball season has “T” number of games. Steven Akronage the town owner and star baseball player hits a lot of home runs. The number of home runs Steven hits in a game is a poisson random variable with parameters μ and is independent of the number of home runs scored during any other game

What is the expected number games where no home runs are hit by Steven?

The satellite signal in your are is not good so you miss out on parts of the baseball game. You observe each home run hit by Steven with probability of P, independently of watching other home runs. Have “H” represent the number of goals scored by Steven in a particular game and “J” the number of home runs you see hit by him in that game. What is P( J = j | H = h). Hence find the P(J = y) for all y ≥ 0

Answer 1

The probability distribution function of a Poisson's random variable is given by

Given,

The probability that no home runs are hit by Steven is

The expected number of games where no home runs are hit by Steven

Given that Steven scores h goals, the probability that you will see j of them is

The probability that J = y is given by

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