Negative Binomial and Geometric Distributions

probability statistics actuarial-science

Solution 1:

Since the number of claims $X\sim \text{Geometric}(\frac 14)$, the desired porbability is $P(X=3)+P(X=4)+P(X=5)=\left(\frac 34\right)^3\frac 14+\left(\frac 34\right)^4\frac 14+\left(\frac 34\right)^5\frac 14=0.2438965$

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