Question

Consider the probability distribution shown below.

x 0 1 2
P(x) 0.55 0.20 0.25

Compute the expected value of the distribution.



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

Answer 1

To get the expected value, multiply each value of x by the corresponding probability P(x), then take the total:

E[X] = ∑ x P(x)

E[X] = 0 • 0.55 + 1 • 0.20 + 2 • 0.25

E[X] = 0 + 0.20 + 0.50

E[X] = 0.70

To get the standard deviation, compute the variance, defined by

Var[X] = E[(X - E[X])²] = E[X²] - E[X]²

Compute the second moment:

E[X²] = ∑ x² P(x)

E[X²] = 0² • 0.55 + 1² • 0.20 + 2² • 0.25

E[X²] = 0 + 0.20 + 1

E[X²] = 1.2

Then the variance is

Var[X] = 1.2 - 0.70²

Var[X] = 0.71

and the standard deviation is the square root of this,

√(Var[X]) ≈ 0.8426