Probability of hitting Homeruns at the Country Club

[mathmajor23]

For this problem, make the assumption that each day is 10 hours long, and that all 7 days of every week you expect the same number of players to be playing all day long.

At the Country Club, players hit a homerun at an average rate of 5 per day.

1) What is the probability that the first ball to get hit for a homerun occurs during the 5th hour of the day?

2) What is the probability that the third ball to get hit for a homerun occurs during the 5th hour of the day? Express your answer as a function of the number e.

3) What is the probability that there are two days in a week where no balls get hit for a homerun?

My attempt:

1) Let X = time the first ball gets hit for a homerun ~ exp(mean 2 hours)
P(4<X<5) =

2) Let Y = time until third balls gets hit for a homerun ~ Gamma(3,2) hours
P(4<Y<5) = ... (not sure how to express answer as a function of e)

3) Let Z = #days in a week where balls get hit for homeruns ~ Poisson(35 balls/7day)
P(Z=5) = ...

 

[scottdave]

I think you can express the Gamma distribution as a sum of Exponential distributions. I need to read up on this again. Take a look at this - https://math.stackexchange.com/ques...on-out-of-sum-of-exponential-random-variables

 

[SammyS]

Do you realize how old this thread is?

 

[berkeman]

Do you realize how old this thread is?

It's okay to reply to old threads that have no replies yet. We've done a lot of work trying to clean up such threads in the past.