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Problem 585

AMC 12 late, AIME early

Algebra Difficulty 5.0 Find the answer

Find the mathematical expectation of the random variable $Z=2 X+4 Y+5$ , if the mathematical expectations of $X$ and $Y$ are known: $M(X)=3, M(Y)=5$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Solution. Using the properties of mathematical expectation (formulas (31) - (33)), we get:

$\begin{aligned} & M(Z)=M(2 X+4 Y+5)=2 M(X)+4 M(Y)+5= \\ & =2 \cdot 3+4 \cdot 5+5=31 \end{aligned}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.