Consider a finite sequence of random values $X=[x_1,x_2,\dots x_n]$. Let…

GATE · 2011 · CS · Computer Science & IT

Consider a finite sequence of random values $X=[x_1,x_2,\dots x_n]$ . Let $\mu_x$ be the mean and $\sigma_x$ be the standard deviation of $X$ . Let another finite sequence $Y$ of equal length be derived from this as $y_i=a*x_i+b$ , where $a$ and $b$ are positive constants. Let $\mu_y$ be the mean and $\sigma_y$ be the standard deviation of this sequence.

Which one of the following statements is INCORRECT?

A.
Index position of mode of $X$ in $X$ is the same as the index position of mode of $Y$ in $Y$
B.
Index position of median of $X$ in $X$ is the same as the index position of median of $Y$ in $Y$
C.
$\mu_y=a \mu_x + b$
D.
$\sigma_y=a \sigma_x + b$

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Consider a finite sequence of random values \(X=[x_1,x_2,\dots x_n]\). Let…