GATE 2022 EE – Question 54
Let the probability density function of a random variable $x$ be given as
$$f(x)=ae^{-2|x|}$$
The value of '$a$' is ________.
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Correct answer: 1
Explanation
The density must integrate to 1: $\int_{-\infty}^{\infty}ae^{-2|x|}dx=2a\int_0^\infty e^{-2x}dx=2a\cdot\frac12=a=1$.