Question

Use the probability distribution for the random variable x to answer the question. х 0 1 2 3 4 5 p(x) 0.3 0.2 0.05 0.15 0.25 0.05 Find u, 02, and o. (Round your standard deviation to two decimal places.) H = 0.2 x 02 = x

Answer 1

ANSWER:

Given data,

x	0	1	2	3	4	5
p(x)	0.3	0.2	0.05	0.15	0.25	0.05

Find $\mu$ , $\sigma ^{2}$ and $\sigma$ .

$\mu$ = E(x) = $\Sigma$ x*p(x)

= (0*0.3)+(1*0.2)+(2*0.05)+(3*0.15)+(4*0.25)+(5*0.05)

= 0+0.2+0.1+0.45+1+0.25

$\mu$ = 2

$\mu$ = 2

E(x^2) = $\Sigma$ ( x^2 *p(x) )

= (0^2*0.3)+(1^2*0.2)+(2^2*0.05)+(3^2*0.15)+(4^2*0.25)+(5^2*0.05)

= 0+0.2+0.2+1.35+4+1.25

= 7

$\sigma ^{2}$ = v(x) = E(x^2) - (E(x) )^2

= 7-(2)^2

=7-4

= 3

$\sigma ^{2}$ = 3

$\sigma$ = sqrt ($\sigma ^{2}$ )= sqrt (3 )

= 1.73

$\sigma$ = 1.73

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