Question

4. 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. a. What probability distributions' properties is this? b. What is the expected value of the random variable x? c. What is the variance of the random variable x?

Answer 1

Answer:

a) We have the mean number of events is interval(5.3 events in 10 minutes), which constitutes the Poisson probability distribution.

b) 5.3

c) 5.3

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:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

a. What probability distributions' properties is this?

We have the mean number of events is interval(5.3 events in 10 minutes), which constitutes the Poisson probability distribution.

b. What is the expected value of the random variable x?

It is known that the mean number of occurrences in ten minutes is 5.3.

So the mean is $\mu = 5.3$

c. What is the variance of the random variable x?

In the Poisson probability distribution, the variance is the same as the mean. So the variance is 5.3.