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P$X$(X)= Me^(-2|x|) + Ne^(-3|x|) is the probability density function for the real random variable X over the entire axis , M andN Both are positive real number . What will be the equation relating M and N?

I considered it as a exponential function and i integrate it -infinity to infinity f($x$) dx=1 But it not generate correct answer . Ans is M+ (2/3)N =1

akash
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1 Answers1

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Taking advantage of symmetry, integrate $Me^{-2x}+Ne^{-3x}$ from $0$ to $\infty$, and set the result equal to $1/2$.

We get $(1/2)M+(1/3)N=1/2$.

Alternately, integrate $Me^{-2x}+Ne^{-3x}$ from $0$ to $\infty$, double, and set the result equal to $1$.

André Nicolas
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