6 5 points Suppose that the continuous random variable X has

6. (5 points) Suppose that the continuous random variable X has the pdf /B for 0 r

Solution

Note that

FX(x) = Integral [fX(x) dx] (-oo, x)

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If x < 0:

FX(x) = Integral [0 dx] (-oo, x)

FX(x) = 0

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If x > 0:

FX(x) = Integral [fX(x) dx] (-oo, x)

FX(x) = Integral [0 dx] (-oo, 0) + Integral [(1/B) exp(-x/B)] (0, x)

FX(x) = [-exp(-x/B)] | (0, x)

FX(x) = -e^(-x/B) + 1

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Thus,

FX(x) = -e^(-x/B) + 1, for 0 < x < oo
0 otherwise [ANSWER]