While Fred is sleeping one night, X legitimate emails and Y spam emails are sent to him. Suppose that X and Y are independent, with X Pois(10) and Y Pois(40). When he wakes up, he observes that he...

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While Fred is sleeping one night, X legitimate emails and Y spam emails are sent to him. Suppose that X and Y are independent, with X

Pois(10) and Y

Pois(40). When he wakes up, he observes that he has 30 new emails in his inbox. Given this information, what is the expected value of how many new legitimate emails he has?

Answered Same DayDec 25, 2021

Answer To: While Fred is sleeping one night, X legitimate emails and Y spam emails are sent to him. Suppose...

David answered on Dec 25 2021

132 Votes

Suppose W = X + Y , we know that W ∼ Poisson with mean = 10 + 40 = 50,
and we can assume that each email from W has probability p of being legitimate,
such that number of legitimate emails is a poisson random variable with mean
= p*50
⇒ 10 = p*50 ⇒ p = 0.2
Given 30 emails have arrived, expected...

SOLUTION.PDF

Sun	Mon	Tue	Wed	Thu	Fri	Sat
30	31	1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30	1	2	3

While Fred is sleeping one night, X legitimate emails and Y spam emails are sent to him. Suppose that X and Y are independent, with X Pois(10) and Y Pois(40). When he wakes up, he observes that he...

Answer To: While Fred is sleeping one night, X legitimate emails and Y spam emails are sent to him. Suppose...

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