Applied Statistics and Probability for Engineers - Geometric and negative binomial distributions (With Answer)

1. Suppose the random variable X has a geometric distribution with p = 0.5. Determine the following probabilities:

2. Suppose the random variable X has a geometric distribution with a mean of 2.5. Determine the following probabilities:

Mean is 2.5 so E (x) is 2.5. In order to get the p value then substitute the E(x) = 2.5 into E(x) = 1/p

2.5 = 1/p

   p = 0.4

3. Suppose that X is a negative binomial random variable with p = 0.2 and r = 4. Determine the following:

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