Question

The random variable Y has the distribution function

F(y)= 0 y<1

ln 0<y<1

1y>1

find the following, i) P( y>2) ii) P(2<y<2)

Answer 1

$F_Y(y) = \begin{cases} 0 &\text{if } y\leq0 \\ ln\ y &\text{if } 0< y\leq1 \\ 1 &\text{if } y>1 \\ \end{cases}$

i) $P(Y>2)= 1-P(Y\leq2)=1-F_Y(2)=0$

ii) $P(1<Y<2)=F_Y(2)-F_Y(1)=1-ln1=1$