Question
Determine k if
$
f(x)=\left\{\begin{array}{ll}
k e^{-\theta x} & \text { for } 0 \leq x<\infty, \theta>0 \\
0 & \text { otherwise }
\end{array}\right.
$
is the p.d.f. of the r.v. $X$. Also find $P\left(X>\frac{1}{\theta}\right)$. Find $M$ if $P(0 < X < M)$=$\frac{1}{2}$
$
f(x)=\left\{\begin{array}{ll}
k e^{-\theta x} & \text { for } 0 \leq x<\infty, \theta>0 \\
0 & \text { otherwise }
\end{array}\right.
$
is the p.d.f. of the r.v. $X$. Also find $P\left(X>\frac{1}{\theta}\right)$. Find $M$ if $P(0 < X < M)$=$\frac{1}{2}$
