Need help with geometric pmf

#1
Hi all,
Here's the problem:

Let X be the number of accidents per week in a factory. Let the probability mass function of X be

f(x) = 1/(x+1) - 1/(x+2), x = 0,1,2,....

Find the conditional probability of X >= 4, given that X>=1.

Thanks!
 

Dason

Ambassador to the humans
#2
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#3
Hi all,
Here's the problem:

Let X be the number of accidents per week in a factory. Let the probability mass function of X be

f(x) = 1/(x+1) - 1/(x+2), x = 0,1,2,....

Find the conditional probability of X >= 4, given that X>=1.

Thanks!
Thanks for the info Dason.

My first thought is to find P(X >=4) for f(x) and P(X >= 1) for f(x). Then I take the results and compute the conditional probability for f(x) P(X >= 4 | X >= 1).

So, P(X >= 4) is equivalent to the SUM (with k=4 to infinity) f(x)^k - f(x=0) - f(x=1)- f(x=2) - f(x=3).
Similarly, (P >= 1) = SUM (w/ k=1 to infinity) f(x)^k - f(x=0).

Is this reasoning correct so far?