Question

If a probability distribution is 5/12, 1/12, 1/4, x, what is the value of x?

A. 1/4

B. 1/6

C. 1/12

D. 1/3

Answer 1

Correct option: A

Explanation:

The properties of a probability distribution are:

1. 0 < P (x = x) < 1.
2. ∑ P (X = x) = 1.

The second property implies that the sum of all the probabilities of a random variable is 1.

Use this property to determine the value of x as follows:

`\sum P(X=k)=(5)/(12)+(1)/(12)+(1)/(4)+x`

`1=(5+1+3+12x)/(12)`

`1=(9+12x)/(12)`

`12=9+12x\\`

`12x=12-9`

`12x=3`

`x=(3)/(12)`

`x=(1)/(4)`

Thus, the missing probability value is
`(1)/(4)`.