Question

Choose a possible probability density function from the given functions:

• A. $f(x) = \begin{cases} 1, & 0 \le x \le 2 \\ 0, & \text{otherwise} \end{cases}$
• B. $f(x) = \begin{cases} e^{-x}, & x \ge 0 \\ 0, & x < 0 \end{cases}$
• C. $f(x) = \begin{cases} \frac{6}{5}x(1+x), & x \ge 0 \\ 0, & x < 0 \end{cases}$
• D. $f(x) = \begin{cases} x(1-x), & 0 \le x \le 1 \\ 0, & \text{elsewhere} \end{cases}$

Hint:

An exponential function profile of the form $f(x) = \lambda e^{-\lambda x}$ for $x \ge 0$ is the standard model for the Exponential Distribution. Recognizing this pattern with $\lambda = 1$ instantly identifies it as a valid normalized probability distribution.

Answer 1

The Correct Option is B