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Chapter 4: Q4.2-2E (page 224)

Suppose that three random variables\({{\bf{X}}_{\bf{1}}}{\bf{,}}{{\bf{X}}_{\bf{2}}}{\bf{,}}{{\bf{X}}_{\bf{3}}}\)froma random sample from a distribution for which the meanis 5. Determine the value of

\({\bf{E}}\left( {{\bf{2}}{{\bf{X}}_{\bf{1}}}{\bf{ - 3}}{{\bf{X}}_{\bf{2}}}{\bf{ + }}{{\bf{X}}_{\bf{3}}}{\bf{ - 4}}} \right)\).

Short Answer

Expert verified

The value of \(E\left( {2{X_1} - 3{X_2} + {X_3} - 4} \right) = - 4\)

Step by step solution

01

Given information

There are three random variables \({X_1},{X_2}\;and\;{X_3}\) from a random distribution. The mean of the distribution is 5.

02

Determine the value.

The value of the given expectation is

\(\begin{array}{c}E\left( {2{X_1} - 3{X_2} + {X_3} - 4} \right) = E\left( {2{X_1}} \right) - E\left( {3{X_2}} \right) + E\left( {{X_3}} \right) - E\left( 4 \right)\\ = 2E\left( {{X_1}} \right) - 3E\left( {{X_2}} \right) + E\left( {{X_3}} \right) - 4\\ = 2 \times 5 - 3 \times 5 + 5 - 4\\ = - 4\end{array}\)

Therefore, the required value is -4.

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Most popular questions from this chapter

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