First slide

Introduction to statistics

Question

Let $X$ be a variate taking values $x_{1}, x_{2}, \dots, x_{n}$ and $Y$ be a variate taking values $y_{1}, y_{2}, \dots, y_{n}$ such that $y_{i} = 6 x_{i} + 3; i = 1, 2, \dots,$ n. If $Var (Y) = 30,$ $σ_{X} =$

Moderate

A

$\frac{5}{\sqrt{6}}$
B

$\sqrt{\frac{5}{6}}$
C

30
D

$\sqrt{30}$

Solution

We have,
$\begin{array}{l} y_{i} = 6 x_{i} + 3; i = 1, 2, \dots, n \\ \Rightarrow Var (Y) = 36 Var (X) \\ \Rightarrow 30 = 36 Var (X) \Rightarrow Var (X) = \frac{5}{6} \Rightarrow σ_{X} = \sqrt{\frac{5}{6}} \end{array}$

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