Statistics Solutions

[All Steps] Let X be a continuous random variable with PDF f(x) and CDF F(x). For a fixed number x_0 such that F(x_0)<1, define the function: g(x)= (f(x))/(1-F(x_0))

Question:

Let X be a continuous random variable with PDF \(f\left( x \right)\) and CDF \(F\left( x \right)\). For a fixed number \({{x}_{0}}\) such that \(F\left( {{x}_{0}} \right)<1\), define the function:

\[g\left( x \right)=\left\{ \begin{aligned} & \frac{f\left( x \right)}{1-F\left( {{x}_{0}} \right)}\text{ for }x\ge {{x}_{0}} \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{for }x<{{x}_{0}} \\ \end{aligned} \right.\]

Prove that g(x) is a PDF.

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Solution: The downloadable solution consists of 1 pages
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