Let the probability density function of a random variable, X, be given as: f_x( x ) = 32e^ - 3xu( x ) + ae^4xu( - x ) where u(x) is the unit step function. Then the value of 'a' and ProbX ≤ 0, respectively, are

This question belongs to Engineering Maths Probability And Statistics

Probability and Statistics

Let the probability density function of a random variable, X, be given as: $${{\text{f}}_{\text{x}}}\left( {\text{x}} \right) = \frac{3}{2}{{\text{e}}^{ - 3{\text{x}}}}{\text{u}}\left( {\text{x}} \right) + {\text{a}}{{\text{e}}^{4{\text{x}}}}{\text{u}}\left( { - {\text{x}}} \right)$$ where u(x) is the unit step function. Then the value of 'a' and Prob{X ≤ 0}, respectively, are

A) 2, $$\frac{1}{2}$$ B) 4, $$\frac{1}{2}$$ C) 2, $$\frac{1}{4}$$ D) 4, $$\frac{1}{4}$$

Answer & Solution

Correct Answer: Option A

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