Multiple choice

Px (x) = M exp (- 2 |x|) - Nexp (- 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. 2M + $\frac{1}{3}$N = 1

  3. M + N = 1

  4. M + N = 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a valid PDF over entire x-axis: ∫{-∞}^{∞} p_x(x)dx = 1. With even function: 2∫{0}^{∞}[Me^{-2x} - Ne^{-3x}]dx = 1. Integrating: 2[M/2 - N/3] = 1, so M - N/3 = 1, giving M - (2/3)N = 1. Note: the expression in option A correctly represents this constraint.

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