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Chapter 4: Q4.1-6E (page 216)

Suppose that a random variable X has a continuous distribution with the p.d.f. has given in Example 4.1.6. Find the expectation of 1/X

Short Answer

Expert verified

\(E\left( {\frac{1}{X}} \right) = 2\)

Step by step solution

01

Given information

X has a continuous distribution having p.d.f. as follows

\(\begin{array}{l}f(x) = 2x\,,0 < x < 1\\\,\,\,\,\,\,\,\,\,\,\,\, = 0,\,{\rm{otherwise}}\end{array}\)

We have to compute \(E\left( {\frac{1}{X}} \right)\)

02

Compute \({\bf{E}}\left( {\frac{{\bf{1}}}{{\bf{X}}}} \right)\)

\(E\left( {\frac{1}{X}} \right)\)

\(\begin{array}{l} = \int_0^1 {\,\frac{1}{x}f(x)dx} \\ = \int_0^1 {2dx} \\ = 2\end{array}\)

So, \(E\left( {\frac{1}{X}} \right) = 2\)

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