Question

Poisson Probability Distribution The random variable x represents the number of phone calls the author receives in a day, and it has a Poisson distribution with a mean of 7.2 calls. What are the possible values of x? Is a value of x = 2.3 possible? Is x a discrete random variable or a continuous random variable?

Short answer

The possible values of X are 0, 1, 2, …….

There is no upper limit for the values that X can hold.

Because X follows the Poisson distribution, which is a discrete probability distribution, it cannot hold a value of 2.3.

Since X follows a discrete probability distribution, X is considered a discrete random variable.

Step-by-step solution

Given information

Here, X represents the number of phone calls received per day. x follows a Poisson distribution. The mean number of phone calls received per day is equal to 7.2.

Values of X

Let X denote the number of phone calls received per day.

It is given that X follows a Poisson distribution with mean equal to 7.2 calls/day.

• The possible values of X are 0, 1, 2, …….

There is no upper limit for the values that X can hold.

• X cannot hold a value equal to 2.3 because X follows Poisson distribution which is a discrete probability distribution. Thus, x cannot hold a decimal value.

• Since X follows a discrete probability distribution, X is considered a discrete random variable.