$(1\mathrm{.}25$ marks$)$

Question $11$: Consider $x$ a random variable on a probability space $,A,P.$ Then:

a$)$ If the distribution function of $x$ has the form $F_x(x)=\frac{x-a}{b-a}$ for $axb$ with $f_{x}axbx{f}_x(x)=c*x^2{f}_x(x)=0c1$ and $f_x(x)=0$ otherwise, $so$ determine the value $ofc$

$(4$ marks$)$

Question $12$: A televisions manufacturer claims that its television life $is11000$ working hours. $We$ select a simple random sample $of$ size $225$ televisions from the factory production, $sowe$ found that the average $of$ televisions life $is10000$ working hours with a standard deviation $of30$ working hours. $If$ the life $of$ televisions $is$ normally distributed, then:$-x,so$ determine the probability density function $(pdf)f_x$ for $axb.$

$b$