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A random variable is known to have a cumulative distribution function . Its density function is:

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Concept:

To analyze the random variable 'x' two functions are used.

1.Probability Distribution Function [F(x)]

2.Probability Density Function [f(x)]

Cumulative Distribution Function

If f(x) is probability density function and F(X) is cumulative distribution function then relation between both of them is:

F(X) = P[X ≤ x] =  = sum of all values less than equal to x.

Probability Density Function

It indicates the distribution of the total probability of various random variables. 

Analysis:

Let U(x) is the unit step function:

= 

= δ(x) - 2x/b U(x)

No option seems to be correct according to the options. 

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