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$\quad P_{X}(x)=M \exp (-2|x|)+N \exp (-3|x|)$ is the probability density function for the real random variable $X$, over the entire $x$ axis. $M$ and $N$ are both positive real numbers. The equation relating $M$ and $N$ is

1. $M+\frac{2}{3} N=1$
2. $2 M+\frac{1}{3} N=1$
3. $M+N=1$
4. $M+N=3$