Question

The probability density function of a continuous random variable is \[ f(x)= \begin{cases} \dfrac35 e^{-3x/5}, & x>0 \\ 0, & x\le0 \end{cases} \] The mean of the distribution is

• A. \(1\)
• B. 5/3
• C. \(2\)
• D. \(3\)

Hint:

For exponential distribution \[ f(x)=\lambda e^{-\lambda x}, \] remember instantly: \[ \text{Mean}=\frac1\lambda, \qquad \text{Variance}=\frac1{\lambda^2}. \]

Answer 1

The Correct Option is B