engineering recuitment NIELIT Scientific Assistant Mock Test 2025 Communication Systems Probability and Random Variable Random Variables
\(\rm{{p_X}\left( x \right){\rm{ }} = {\rm{ }}Mexp\left( { - 2|x|} \right){\rm{ }} + {\rm{ }}Nexp\left( { - 3|x|} \right)}\) is the probability density function for the real random variable \(\rm{X}\), over the entire x – axis. \(\rm{M}\) and \(\rm{N}\) are both positive real number. The equation relating \(\rm{M}\) and \(\rm{N}\) is:
1
\(\rm M + \frac{2}{3}N = 1\)
2
\(\rm 2M + \frac{1}{3}N = 1\)
3
\(\rm M{\rm{ }} + {\rm{ }}N{\rm{ }} = 1\)
4
\(\rm M{\rm{ }} + {\rm{ }}N{\rm{ }} = 3\)