Question

The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The appropriate probability distribution for the random variable is

Answer 1

Answer:

A Poisson distribution, with λ=5.3

$P(x) = \frac{\lambda^{x} *e^{-\lambda}}{x!}$

Step-by-step explanation:

For this type of random variables, a Poisson distribution is the most adecuate.

If the number of occurrences in ten minutes is 5.3, we can define the parameter λ=5.3 and the probability function as:

$P(x) = \frac{\lambda^{x} *e^{-\lambda}}{x!} =\frac{5.3^{x} *e^{-5.3}}{x!} \approx\frac{0.005*5.3^{x}}{x!}$