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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.)

User MobileGuy
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1 Answer

4 votes

Answer:

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

User Parakoos
by
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