Question

Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.) x P(x) 6 0.10 12 0.35 18 0.25 24 0.30

Answer 1

Answer:

Mean = 16.5

Variance = 35.55

Step-by-step explanation:

           x      P(x)        x. P(x)     x²            x². P(x)

          6      0.10          0.6      36            3.6

         12     0.35          4.2       144           50.4

        18     0.25           4.5       324            81

        24     0.30          7.2        576         172.8

                  ∑x P (x)  16.5         ∑x² P (x) 307.8

The expected value of x E[X] gives the mean where X is the discrete random variable with the given probabilities.

Mean is given by  E(X)=  ∑x P (x) =  16.5

Similarly the variance is also calculated using the expected value of X and X².

Variance is given= E(X)²-  [E(X)]²= 307.8- (16.5)²=  307.8-272.25 = 35.55