Compute $E(g)$, where $g=2-|f|$ if $|f|lephi$ and $g=0$ otherwise, and $phi$ is uniformly distributed over...












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$$Eleft[begin{cases} 2-|f|,& |f|lephi\\ 0,& text{else} end{cases}right]$$ where $phi$ is uniform distribution over $[0,1]$



I find it difficult to calculate it using the integral. it's hard for me to understand the format of the integral because we are summing on $phi$ when it's connected to range of the function.






probability-theory expected-value







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-1












$begingroup$


$$Eleft[begin{cases} 2-|f|,& |f|lephi\\ 0,& text{else} end{cases}right]$$ where $phi$ is uniform distribution over $[0,1]$



I find it difficult to calculate it using the integral. it's hard for me to understand the format of the integral because we are summing on $phi$ when it's connected to range of the function.






probability-theory expected-value







share|cite|improve this question











$endgroup$












  • $begingroup$
    Let us continue this discussion in chat.
    $endgroup$
    – Mr.OY
    Jan 10 at 16:20














-1












-1








-1





$begingroup$


$$Eleft[begin{cases} 2-|f|,& |f|lephi\\ 0,& text{else} end{cases}right]$$ where $phi$ is uniform distribution over $[0,1]$



I find it difficult to calculate it using the integral. it's hard for me to understand the format of the integral because we are summing on $phi$ when it's connected to range of the function.






probability-theory expected-value







share|cite|improve this question











$endgroup$




$$Eleft[begin{cases} 2-|f|,& |f|lephi\\ 0,& text{else} end{cases}right]$$ where $phi$ is uniform distribution over $[0,1]$



I find it difficult to calculate it using the integral. it's hard for me to understand the format of the integral because we are summing on $phi$ when it's connected to range of the function.






probability-theory expected-value




probability-theory expected-value






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 9 at 17:17









Did

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247k23223460










asked Jan 9 at 17:02









Mr.OYMr.OY

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16410












  • $begingroup$
    Let us continue this discussion in chat.
    $endgroup$
    – Mr.OY
    Jan 10 at 16:20


















  • $begingroup$
    Let us continue this discussion in chat.
    $endgroup$
    – Mr.OY
    Jan 10 at 16:20
















$begingroup$
Let us continue this discussion in chat.
$endgroup$
– Mr.OY
Jan 10 at 16:20




$begingroup$
Let us continue this discussion in chat.
$endgroup$
– Mr.OY
Jan 10 at 16:20










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