Question

Asked May 11, 2019

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Scale the function to convert it into a probability density function. Then find the expected value of a random variable with that density. If not possible, write undefined

Step 1

Let K be the required scaling factor to convert the given function into a probability density function (PDF).

Hence, PDF = P(x) = k.f(x) = 6Ke^{-8x} if x> 0 and 0 otherwise.

Step 2

If P(x) is the PDF then integral of P(x) over x = -∞ to x = ∞ should be 1. Please see the whiteboard.

Hence, 3K /4 = 1

hence, K = 4 / 3

Step 3

So, the pdf is: P(x) = 6 x 4 / 3 x e-8x for x &g...

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