1.The following table shows part of the probability distribution for a random variable x.

x P(x)

00.2

1?

20.15

3?

40.15

a. The mean of the above distribution is known to be 1.8 (i.e., E(x) = 1.8). Determine P (1) and P (3).

P(1) = 0.3

p(3) = 0.2

b. Compute the variance and the standard deviation for the above probability distribution

Variance = 1.86

What is the standard deviation for this probability distribution? Please explain in detail how to solve.