First slide

Introduction to statistics

Question

If $X$ is a variate taking values $x_{1}, x_{2}, \dots, x_{n}$ .Y is another variate taking values $y_{1}, y_{2}, \dots, y_{n}$ such that $y_{i} = 2 x_{i} + 3$ and $σ_{Y} = 8$ , then the variance of variable Z taking values $\frac{3}{2} x_{i}; i = 1, 2, \dots, n$ , is

Moderate

A

24
B

36
C

6
D

18

Solution

We have,
$\begin{array}{l} y_{i} = 2 x_{i} + 3; i = 1, 2, \dots n \\ ∴ Var (Y) = 4 Var (X) \\ \Rightarrow 64 = 4 Var (X) \Rightarrow Var (X) = 16 \end{array}$
Now,
$\begin{array}{l} z_{i} = \frac{3}{2} x_{i}; i = 1, 2, \dots, n \\ \Rightarrow Var (Z) = \frac{9}{4} Var (X) = \frac{9}{4} \times 16 = 36 \end{array}$

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