# Probability: Random Variable and Probability Density Function

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Problem 1: A random variable X takes values between 0 and infinity with a probability density function

f(x) = A + Be^(-x) for 0 <= x <= infinity.

a) find A and B

b) find expected value of X

c) what is the median of X?

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##### Solution Summary

The expected value and median of a random variable are found. The full calculations are shown.

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a.)

because,

integration(0 to infinity)[f(x) dx] = 1 (total probability = 1)

=>integration(0 to infinity)[(A+B*exp(-x)) dx] = 1

=> A*x - B*exp(-x)|(0 to infinity) = 1

=> A = 0 ( because x value is from 0 to infinity, because of ...

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- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India

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