Probabi Question

👨🏻‍🏫 學術台數學

Gary

2010-04-20 10:42 am

The number of people who enter a library in a given hour is a Poisson random variable with parameter 入=10.
Find the condition probability that at most 3 women enter the library, given 10 men entered in that hour.
What assumptions have been made?

更新1:

Re myisland8132, Why is λ changed from 10 to 5?

回答 (1)

myisland8132

2010-04-20 9:26 pm

✔ 最佳答案

Assume that the man (X) or woman (Y) enter a library with equal probability, then
λ_x=λ_y=5

the condition probability that at most 3 women enter the library, given 10 men entered in that hour

=P(X=10 and Y<=3)/P(X=10)

=P(X=10)P(Y<=3)/P(X=10)

=P(Y<=3)

=(1+5+25/2+125/6)e^(-5)

=39.3e^(-5)

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