Question

Determine whether the following can serve as the probability distribution of a random variable X.

1. P(X)= 1/7 for x=1, 2, 3, 4, 5, 6, 7

2.P(X)=x-2/3 for x = 1, 2, 3, 4, 5

Answer 1

1.

$$\sum _ip(x_i)=\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{7}+\dfrac{1}{7}=1$$

The following can serve as the probability distribution of a random variable $X.$

2.

$$\sum _ip(x_i)=1-\dfrac{2}{3}+2-\dfrac{2}{3}+3-\dfrac{2}{3}$$ $$+4-\dfrac{2}{3}+5-\dfrac{2}{3}=\dfrac{35}{3}\not=1$$

The following cannot serve as the probability distribution of a random variable $X.$