Question
Asked Oct 1, 2019
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Find the variance of the random variable Y where
3
)2,0y < 2
fr(u)
8
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Find the variance of the random variable Y where 3 )2,0y < 2 fr(u) 8

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Expert Answer

Step 1

The given that the probability density function of the random variable Y is,

f(y)
0 y 2
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f(y) 0 y 2

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Step 2

The required formula for the finding the variance of the random variable y where is,

Var (Y) E(2)-E(Y)
E(Y)=W:(y)dy aysb
a
E(y2)=Jy'(v)cdya<ysb
asysb
a
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Var (Y) E(2)-E(Y) E(Y)=W:(y)dy aysb a E(y2)=Jy'(v)cdya<ysb asysb a

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Step 3

The required value of E (...

E(Y)=, (v)d
2
3
dy
0
3
3
84
0
3
(4)
3
2
|
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E(Y)=, (v)d 2 3 dy 0 3 3 84 0 3 (4) 3 2 |

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