If $f(x) = \lambda e^{- ax}(a 0)$ for $0 \leq x

Question

If $f(x) = \lambda e^{- ax}(a > 0)$ for $0 \leq x < \infty\$is a prabability density, then $\lambda$ is equal to

Dr. Abubacker · Accepted Answer

(a)
Given, $f(x) = \lambda e^{- ax},for\ 0 \leq x < \infty\ and\ a > 0$
$	herefore\int_{0}^{\infty}{\lambda e^{- ax} = 1\ \ \lbrack\because}\ sum\ of\ total\ distribution\ is\ onebrack$
$\Rightarrow \ \lambda\left\lbrack \frac{e^{- ax}}{- a} ightbrack_{0}^{\infty} = 1$
$\Rightarrow \ \lambda\left\lbrack 0 + \frac{1}{a} ightbrack = 1 \Rightarrow \lambda = a$

Q. If $f(x) = \lambda e^{- ax}(a > 0)$ for $0 \leq x < \infty\$is a prabability density, then $\lambda$ is equal to

Explanation

Reviewed by Dr. Abubacker

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