Question

suppose that the number of customers that enter a bank in an hour is poisson random variable, and suppose that P(X=0)=0.05. Determine the mean andvariance of X?

Answer 1

To determine the mean and variance of a Poisson random variable where the probability of zero events is 0.05, use the formula P(X=0) = e^(-mean) to solve for the mean. This value will also represent the variance, because in a Poisson distribution, the mean equals the variance.

Step-by-step explanation:

If the number of customers that enter a bank in an hour is a Poisson random variable, and P(X=0)=0.05, you can determine the mean (λ) of the distribution using the formula for the probability of zero events: P(X=0) = e^(-λ). By setting P(X=0) to 0.05 and solving for λ, you get λ = -ln(0.05). This mean is also the variance of the Poisson distribution, as for a Poisson random variable, the mean is equal to the variance.