Question

The answers you see in red are incorrect.

Given the cumulative density function F(x) k- , x ,1, F )0 for x< 1, for some fixed number k, 1, F(x) = 0 for z 〈 1, for some fixed number k, What is k? 1.75 1.75 What is Tmin 75 .75 What is P(x 4)? 5/14 .5714 What is P(2 < X 5)?

Answer 1

$We~know,~F(\infty)=1~or,~k-\frac{1}{\left \lfloor \infty \right \rfloor}=1~or,~k=1\\ P(X=4)=F(4)-F(4-)=k-\frac{1}{4}-k&plus;\frac{1}{3}=1/12=0.0833\\ P(2<X\leq 5)=F(5)-F(2)=k-\frac{1}{5}-k&plus;\frac{1}{2}=\frac{3}{10}=0.3\\ Since~F(x_{min})=0~so~k-\frac{1}{\left \lfloor x_{min} \right \rfloor}=0~or,~\left \lfloor x_{min} \right \rfloor=1\\ So,~1\leq x_{min}<2$