First slide

Introduction to statistics

Question

The mean and variance of n values of a variable x are 0 and 0², respectively. If the VariabLe y = x² then mean of y is

Moderate

A

$σ$
B

$σ$ ²
C

1
D

None of these

Solution

Given that, mean = 0 and variance $= σ^{2} (for x)$ Therefore, variance $= σ^{2} = \frac{{Σx}^{2}}{n} - {(\frac{Σx}{n})}^{2}$
$\begin{array}{l} \Rightarrow σ^{2} = \frac{{Σx}^{2}}{n} - 0 \Rightarrow σ^{2} = \frac{{Σx}^{2}}{n} \\ Now, y = x^{2} \\ \Rightarrow Σy = {Σx}^{2} \\ ∴ \bar{y} = \frac{{Σx}^{2}}{n} = σ^{2} \end{array}$

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