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

question 87

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

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