This might be a stupid question, but how I can calculate the expected value $\operatorname{E}(-1X)$ and variance $\operatorname{Var}(-1X)$ for example in a case in which $X\sim N(100,0.1^2)$?
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$\begingroup$ Is it a homework? $\endgroup$– TimCommented Aug 25, 2020 at 9:54
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$\begingroup$ A part of assignment. Other parts are clear but this keeps me stuck... $\endgroup$– KaemCommented Aug 25, 2020 at 9:56
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1$\begingroup$ See en.wikipedia.org/wiki/Expected_value#Linearity and en.wikipedia.org/wiki/Variance#Basic_properties $\endgroup$– Glen_bCommented Aug 25, 2020 at 11:50
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1 Answer
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We have the general rules
$$ E[a + bX] = a + bE[X] $$
and
$$ Var[a + bX] = b^2 Var[X] $$
So in this case,
$$ E[-1X] = -1 \cdot 100 = -100 $$
and
$$ Var[-1X] = (-1)^2 \cdot 0.1^2 = 0.1^2 $$
answered Aug 25, 2020 at 10:45