Question

Suppose X ~ U(37,51), T ~ EXP(0.008) and Y ~G(54,0.25).Calculate the following:

    (a) The constant m if P(X < m) = 0.63

Answer 1

Solution:

X ~ U(37,51)

(a) $f(x)=\dfrac{1}{51-37}=\dfrac{1}{14}$

$P(X<m)=\dfrac{m-0}{14}=0.63$

$\Rightarrow \dfrac{m}{14}=0.63 \\ \Rightarrow m=0.63\times 14=8.82$