Question

Is a probability distribution defined if the only possible values of a random variable are 0, 1,2, 3, and P(0) = P(1) = P(2) = P(3) = 1/3?

Short answer

No, the probability distribution is not defined if the only possible values of a random variable are 0, 1,2, 3, and $P\left(0\right)=P\left(1\right)=P\left(2\right)=P\left(3\right)=\frac{1}{3}$.

Step-by-step solution

Given information

The possible values of a random variable are 0,1,2,3.

The probabilities are given as,

$P\left(0\right)=P\left(1\right)=P\left(2\right)=P\left(3\right)=\frac{1}{3}$

.

Identify the requirements for a probability distribution

The requirements are as follows:

1)The variable x is anumerical random variable.

2)The sum of the probabilities is computed as,

$$\begin{gathered} \sum P\left(x\right)=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3} \\ =1.333 \end{gathered}$$

Therefore,the sum of the probabilities is not equal to 1 and is greater than 1.

3) Each value of P(x) is between 0 and 1.

Therefore, the probability distribution is not appropriately defined.