Suppose that the number of customers who enter a post office in a 49-minute period is a Poisson random variable and that P(X = 0) = 0.03. Determine the (a) mean and (b) variance of X. Round your answers to two decimal places (e. g. 98.76).

Both the mean and the variance are equal to 3.51

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

is the Euler number

is the mean in the given time interval.

The mean and the variance are equal, so is also the variance.

We have that:

So

Applying ln to both sides

Multiplying by -1

answer: answer

step-by-step explanation:

b. x + 1

step-by-step explanation:

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