Discrete Random Variables (DRV) - Linear Combinations of Random Variables
Discrete Random Variables (DRV) - Linear Combinations of Random Variables
TGM Original Questions
The discrete random variable \(X\) takes values \(1,2,\ldots,9\), with the following probability distribution.
\[P(X=x) = \begin{cases} ax & 1 \le x \le 5 \\ a(10-x) & 6 \le x \le 9 \\ 0 & \text{otherwise} \end{cases}\]
Find the value of the constant \(a\), \(\mathrm{E}(X)\), \(\mathrm{Var}(X)\), \(\mathrm{E}(2X-3)\) and \(\mathrm{Var}(2X-3)\).
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Answer:\(a=\frac1{25}\), \(\mathrm E(X)=5\), \(\mathrm{Var}(X)=4\), \(\mathrm E(2X-3)=7\), and \(\mathrm{Var}(2X-3)=16\).
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