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If a random communication signal has PDF given by P(X) = 2ae-b|x| for all x, -∞ < x < +∞ then :

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  1. b = 2a
  2. b = 4a
  3. b = a/2
  4. b = 0

Answer (Detailed Solution Below)

Option 2 : b = 4a
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Detailed Solution

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Concept:

For any valid probability density function (PDF), the total area under the curve must be 1:

Given:

Calculation:

Since the function is even (depends on ), integrate over the positive side and double it:

 

Set equal to 1 (normalization condition):

Hence, the correct option is 2

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