A Random Variable X Has Probability Density Function F(x) = $k e ^ { - k x }$

Multiple Choice

A random variable X has probability density function f(x) = $k e ^ { - k x }$ (x ≥ 1) for some constant k. Suppose that $\operatorname { Pr } ( 1 \leq X \leq 2 ) = \frac { 1 } { 4 }$ , what is the value of k?

A) $\frac { 1 } { 2 }$ ln 2
B) $\frac { 3 } { 2 }$ ln 2
C) $\frac { 1 } { 4 }$
D) ln 2
E) none of these