$3.$When you are filling up your glass using the demijohn at your house,

you have noticed the erratic behavior executed by the demijohn. The water

either spills or the glass is not filled completely. You decide to measure the

amount of water your demijohn lets you have and let $x$ denote the differ$-$

ence of water amount in units of $c{m}^3.$ Rigorously defined, let minuend and

subtrahend be amount of water desired by you and the amount provided by

the demijohn respectively. You guess that $xU[-2,2].$ Your aunt asks

some questions, please help her understand these.

a$)P(x=0)$

b$)P(x0\mathrm{.}7)$

c$)P(x-1\mathrm{.}3)$

d$)P(x-1\mathrm{.}3|x<0\mathrm{.}5)$

e$)$ Letting $Y$ denote the random variable on the $2^{nd}$ question with rate

$)-0\mathrm{.}8,Y<8|x|<0,Y>(4$

The random variable from $2$nd question is $=$ Let X ~ Exponential$(4)$