$$\text { For random variables } x \text { and } y \text {, if } y = a + b x \text {, then } \sigma _ { y } = a + b \sigma _ { x }$$

Name: \[\text { For random variables } x \text { and } y \text {, if } y = a + b x \text {, then } \sigma _ { y } = a + b \sigma _ { x }\]
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The correct formula should be $\sigma_y = |b|\sigma_x$ because when the sign of $b$ changes, it can change the variability of $y$. Adding a constant term ($a$) does not affect the variability.

For random variables x and y, if y=a+bx, then σy=a+bσx\text { For random variables } x \text { and } y \text {, if } y = a + b x \text {, then } \sigma _ { y } = a + b \sigma _ { x } For random variables x and y, if y=a+bx, then σy​=a+bσx​

$\text { For random variables } x \text { and } y \text {, if } y = a + b x \text {, then } \sigma _ { y } = a + b \sigma _ { x }$