Question $4$

Suppose $x$ is a continuous random variable with the following probability density function $($pdf$)$:

$CCCx\%100==59x,E[x]P(0\mathrm{.}2.$ Assign your answer

$to$ the variable ans

$In[]$: # your code here

fail$()$ # $No$ Answer $-$ remove $if$ you provide $an$ answer

$In[]$: ## check whether the $2nd$ & $3rd$ dec. digits are $59$

$if(tes{t}_t$hat $(desc="",$ code $=\{$

$expec{t}_e$qual $((floor(ans*{10}^3)\%100==59),$ TRUE$)$

$\})$ TRUE$)$ stop$("Sorry,$ your answer $is$ incorrect."$)$

$In[]$: # test whether the answer $is$ correct $(hidden$ test$)$

Part $c)$

Determine the expected value $ofx,E[x].$ Assign your answer $to$ the variable $EX$

$In[]$: # your code here

fail$()$ # $No$ Answer $-$ remove $if$ you provide $an$ answerf$(x)=\{[C(x-x^3),0$

where $Cis$ a constant.

Part $a)$

Determine the value $of$ the constant, $C.$ Assign your answer $to$ the variable $C(uppercase)$

$In[]$: # your code here

fail$()$ # $No$ Answer $-$ remove $if$ you provide $an$ answer

$In[19]$: # test whether the answer $is$ correct $(hidden$ test$)$

Part $b)$

Determine the $(exact)$ probability that $xis$ between $0\mathrm{.}2$ and $0\mathrm{.}5.$ That $is,$ determine $P(0\mathrm{.}2.$ Assign your answer

$to$ the variable ans

$In[]$: # your code here

fail$()$ # $No$ Answer $-$ remove $if$ you provide $an$ answer

$In[]$: ## check whether the $2nd$ & $3rd$ dec. digits are $59$

$if(tes{t}_t$hat $(desc="",$ code $=\{$

$expec{t}_e$qual $((floor(ans*{10}^3)\%100==59),$ TRUE$)$

$\})$ TRUE$)$ stop$("Sorry,$ your answer $is$ incorrect."$)$

$In[]$: # test whether the answer $is$ correct $(hidden$ test$)$

Part $c)$

Determine the expected value $ofx,E[x].$ Assign your answer $to$ the variable $EX$

$In[]$: # your code here

fail$()$ # $No$ Answer $-$ remove $if$ you provide $an$ answer