Question

true or false? Give reason
If X has the distribution N(10, 9) and if Y = 5X − 3, then Y has distribution
N(53,84) .

Answer 1

Answer on Question#65568 – Math – Statistics and Probability

Question. True or false? Give reason.

If $X$ has the distribution $N(10,9)$ and if $Y = 5X - 3$, then $Y$ has the distribution $N(53,84)$.

Solution. Since $E(X) = 10$ by condition then using the properties of mathematical expectation (see https://en.wikipedia.org/wiki/Expected_value#Properties) we get:

$$E(Y) = E(5X - 3) = E(5X) - 3 = 5E(X) - 3 = 5 \cdot 10 - 3 = 47 \neq 53, \quad \text{and} \quad \text{original statement is false}.$$

Answer. False.

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