Suppose f(x)=0.125x for 0&lt;x&lt;4. determine the mean and variance of X.

Mean&nbsp;[E(x)]&nbsp;of&nbsp;x&nbsp;The mean formula is given by,E(x)=∫xf(x)&nbsp;dx&nbsp;&nbsp;=∫40x⋅0.125x&nbsp;dx&nbsp;&nbsp;=∫40x2⋅0.125x&nbsp;dx&nbsp;&nbsp;=0.125=∫40x2&nbsp;dx&nbsp;&nbsp;=0.125[x33]04&nbsp;{since&nbsp;∫xn&nbsp;dx&nbsp;=xn+1n+1}&nbsp;=0.125[433−0]&nbsp;=0.125(643)&nbsp;E(x)=83&nbsp;or&nbsp;2.667

The formula for varience of x is given by, Varience(x)= E[x2]−[E[x]]2 to find E[x2]: E[x2]=∫xx2f(x)dx =∫04x2⋅0.125xdx =∫04x3⋅0.125dx =0.125∫04x3dx =0.125[x4x]04sin⁡cePSK∫xndx=(xn+1)n+1} =0.125[444−0] =0.125⋅43 E[x2]=8 Thus =E[x2]−[E[x]]2 We know that E[x2]=8 and E[x]=2.667 Thus =8−(2.667)2 =8−7.113 =0.887 Varriance of x 0.887

Mean&nbsp;[E(x)]&nbsp;of&nbsp;x&nbsp;The mean formula is given by,E(x)=∫xf(x)&nbsp;dx&nbsp;&nbsp;=∫40x⋅0.125x&nbsp;dx&nbsp;&nbsp;=∫40x2⋅0.125x&nbsp;dx&nbsp;&nbsp;=0.125=∫40x2&nbsp;dx&nbsp;&nbsp;=0.125[x33]04&nbsp;{since&nbsp;∫xn&nbsp;dx&nbsp;=xn+1n+1}&nbsp;=0.125[433−0]&nbsp;=0.125(643)&nbsp;E(x)=83&nbsp;or&nbsp;2.667

The formula for varience of x is given by, Varience(x)= E[x2]−[E[x]]2 to find E[x2]: E[x2]=∫xx2f(x)dx =∫04x2⋅0.125xdx =∫04x3⋅0.125dx =0.125∫04x3dx =0.125[x4x]04sin⁡cePSK∫xndx=(xn+1)n+1} =0.125[444−0] =0.125⋅43 E[x2]=8 Thus =E[x2]−[E[x]]2 We know that E[x2]=8 and E[x]=2.667 Thus =8−(2.667)2 =8−7.113 =0.887 Varriance of x 0.887

Find out the answer to "Suppose f(x)=0.125x for 0<x<4. determine the mean and..."

socorraob

Answered question

2021-12-12

Suppose

f (x) = 0.125 x

for

0 < x < 4

. determine the mean and variance of X.

Answer & Explanation

Hector Roberts

Beginner2021-12-13Added 31 answers

Mean $[E (x)]$ of $x$
The mean formula is given by,
$E (x) = \int_{x} f (x) d x$
$= \int_{4}^{0} x \cdot 0.125 x d x$
$= \int_{4}^{0} x^{2} \cdot 0.125 x d x$
$= 0.125 = \int_{4}^{0} x^{2} d x$
$= 0.125 {[\frac{x^{3}}{3}]}_{0}^{4}$ {since $\int x^{n} d x = \frac{x^{n + 1}}{n + 1}$ }
$= 0.125 [\frac{4^{3}}{3} - 0]$
$= 0.125 (\frac{64}{3})$
$E (x) = \frac{8}{3}$ or $2.667$

Bertha Jordan

Beginner2021-12-14Added 37 answers

The formula for varience of x is given by,
Varience(x)=

E [x^{2}] - {[E [x]]}^{2}

to find

E [x^{2}]

E [x^{2}] = \int_{x} x^{2} f (x) d x

= \int_{0}^{4} x^{2} \cdot 0.125 x d x

= \int_{0}^{4} x^{3} \cdot 0.125 d x

= 0.125 \int_{0}^{4} x^{3} d x

= 0.125 {[\frac{x^{4}}{x}]}_{0}^{4} \frac{\sin c e P S K \int x^{n} d x = (x^{n + 1})}{n + 1}

}

= 0.125 [\frac{4^{4}}{4} - 0]

= 0.125 \cdot 4^{3}

E [x^{2}] = 8

Thus

= E [x^{2}] - {[E [x]]}^{2}

We know that

E [x^{2}] = 8

and

E [x] = 2.667

Thus

= 8 - {(2.667)}^{2}

= 8 - 7.113

= 0.887

Varriance of x

0.887

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