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My spam filter flags 2% of my emails, which I assume arrive in my inbox at...

My spam filter flags 2% of my emails, which I assume arrive in my inbox at random. Let the random variable Y be the number of emails I receive until I see the second spam message (including the second spam message). Write down the probability mass function of Y as a formula. [Hint: write down p(y) for a few cases and then try to guess a formula for a general y from the pattern]

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Answer #1

Suppose "p"be the probability that emails is spam is.

i.e p=0.02

Let Y be the number of emails receive untill to see the second spam message. Therefore the distribution of Y is negative binomial with probability p=0.02 and r=2,

Where r is the rth success.

The probability mass function of Y is

, y=r,r+1,r+2,...

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