Question

Consider the probability distribution shown below. x 0 1 2 P(x) 0.15 0.80 0.05 Compute the expected value of the distribution. (Enter a number.) Compute the standard deviation of the distribution. (Enter a number. Round your answer to four decimal places.)

Answer 1

Expected value =0.9

Standard deviation = 0.4359

Explanation:

Let's use the formula to find expected value or mean.

Expected value =Σ x *P(x)

x 0 1 2

P(x) ) .15 .8 .05

So, expected value = (0)(0.15) +1(0.8)+2(0.05)

= 0 +0.8 +0.1

=0.9

Expected value =0.9

Now, let's find standard deviation

x
`(x- E(x))^(2)`
`(x-E(x))^(2) *p(x)`

0
`(0-0.9)^(2)`
`(0-0.9)^(2) *0.15` =0.1215

1
`(1-0.9)^(2)`
`(1-0.9)^(2) *0.8` =0.008

2
`(2-0.9)^(2)`
`(2-0.9)^(2) *0.05` =0.0605

Now, add the last column together and then take square root to find standard deviation.

Standard deviation of the distribution =
`√(0.1215+0.008+0.0605))`

Simplify it, so standard deviation =0.4358898...

Round the answer to nearest four decimal places

Standard deviation = 0.4359