Question

For what value of the constant \(k\), the function \[ f(x)= \begin{cases} kxe^{-2x}, & x>0 \\ 0, & \text{otherwise} \end{cases} \] is a probability density function?

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. \(4\)

Hint:

For PDF questions: \[ \boxed{\int_0^\infty x^n e^{-ax} dx = \frac{n!}{a^{n+1}}} \] Always ensure the total area under the curve equals 1.

Answer 1

The Correct Option is B