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Given the probability density function

$$ f(x) = \begin{cases} \frac{cx}{3}, & 0 \leq x < 3, \\ c, & 3 \leq x \leq 4, \\ 0 & \text{ otherwise} \end{cases} $$

I have found $c$ to be $0.4$ and $E(X)$ to be $2.6$. But I'm being asked to find $E(3X - 5)$ and I'm unsure of what to do.

Michael Hardy
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jbbrsh1494
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    Are you familiar with the phrase "linearity of expectation"? (i.e., the expectation is a linear operator: $\mathbb{E}[aX+b] = a\mathbb{E}[X]+b$ for any constants $a,b$) – Clement C. May 15 '14 at 19:43
  • use the definition of expectation, you dont need to know something more than this. – Seyhmus Güngören May 15 '14 at 19:48

1 Answers1

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$$\mathbf E(3\mathbf X-5)=3\mathbf E(\mathbf X)-5=3(2.4)-5=2.2$$

Asaf Karagila
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Arun Eminm
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