Question

Consider the probability distribution shown below.

x	0	1	2
P(x)	0.45	0.20	0.45

(a) Compute the expected value of the distribution.

(b) Compute the standard deviation of the distribution


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

Answer 1

Given data is false

because $\Sigma p(x)=0.45+0.20+0.45=1.10\neq 1$

if our assumption is true then

(a) $E(x)=x.P(x)=0(0.45)+1(0.20)+2(0.45)=0+0.2+0.9=1.1$

(b)$\sigma ^{2}=\Sigma x^{2}.P(x)=0(0.45)+1(0.20)+4(0.45)-1.1^{2}=0.79$

Standard deviation $\sigma =\sqrt{0.79}=0.8888$