Statistics Question

[Jimbo123]

Hi All,

Need some help with the following questions

For the random variable X, it is known that E(X) = 6 and Var(X) = 2
a Write down E (2X), Var (2X) and σ for the new distribution 2X.
b Write down E(X + 5), Var(X + 5) and σ for the new distribution X + 5.
c Write down E (3X − 1), Var (3X − 1) and σ for the new distribution 3X − 1.

Any help is much appreciated

[RuiAce]

Hi All,

Need some help with the following questions

For the random variable X, it is known that E(X) = 6 and Var(X) = 2
a Write down E (2X), Var (2X) and σ for the new distribution 2X.
b Write down E(X + 5), Var(X + 5) and σ for the new distribution X + 5.
c Write down E (3X − 1), Var (3X − 1) and σ for the new distribution 3X − 1.

Any help is much appreciated

All of these can be solved using the following formulae:
\begin{align*}
\operatorname{E}(aX+b)&=a\operatorname{E}(X)+b\\
\operatorname{Var}(aX)&=a^2\operatorname{Var}(X)\\
\operatorname{Var}(X+b)&= \operatorname{Var}(X)
\end{align*}
where \(X\) is the random variable, and \(a\) and \(b\) are constants.

That should be all you need. If you require any further assistance, please post any relevant progress/brainstorm.