Question

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

Answer 1

Answer:

Correct option: A

Step-by-step 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:

$\sum P(X=k)=\frac{5}{12}+\frac{1}{12}+\frac{1}{4}+x$

                 $1=\frac{5+1+3+12x}{12}$

                 $1=\frac{9+12x}{12}$

               $12=9+12x$

             $12x=12-9$

             $12x=3$

                 $x=\frac{3}{12}$

                 $x=\frac{1}{4}$

Thus, the missing probability value is $\frac{1}{4}$.