probabilities. Please help

Question

Consider the probability distribution shown below.

x	0	1	2
P(x)	0.75	0.20	0.05

Compute the expected value of the distribution. 

 

Compute the standard deviation of the distribution. (Round your answer to four decimal places.) 

Answer 1

The expected value is the sum of the x values multiplied by their respective probability:

0(.75) + 1(.2) + 2(.05) = 0 + .2 + .1 = .3

The standard deviation is found by taking each x value subtracting the mean (found above), squaring that difference, then multiplying by the probability. The sum of these is the variance, so taking the square root is the standard deviation.

(0-.3)^2 * .75 + (1-.3)^2 * .2 + (2-.3)^2 * .05 = .31

square root of .31 = .5568