If m and σ 2 are the mean and variance of the random variable X . whose distribution is given by x 0 1 2 3 P x 1 / 3 1 / 2 0 1 / 6 then

Question

If m and &#963; 2 are the mean and variance of the random variable X . whose distribution is given by x 0 1 2 3 P x 1 / 3 1 / 2 0 1 / 6 then

Aicharya · Accepted Answer

Given, distribution is x 0 1 2 3 P x 1 / 3 1 / 2 0 1 / 6 &#8756; &#160; Mean, m = &#8721; i = 1 4 p i x i = 0 &#215; 1 3 + 1 &#215; 1 2 + 2 &#215; 0 + 3 &#215; 1 6 = 0 + 1 2 + 0 + 1 2 = 1 Variance, &#963; 2 = &#8721; i = 1 4 p i x 1 - m 2 = 1 3 0 - 1 2 + 1 2 1 - 1 2 + 0 2 - 1 1 + 1 6 3 - 1 2 = 1 3 + 0 + 0 + 2 3 = 1 &#8756; &#160; m = &#963; 2 = 1

$x$	$0$	$1$	$2$	$3$
$P (x)$	$1 / 3$	$1 / 2$	$0$	$1 / 6$

$x$	$0$	$1$	$2$	$3$
$P (x)$	$1 / 3$	$1 / 2$	$0$	$1 / 6$

If m and σ 2 are the mean and variance of the random variable X . whose distribution is given by x 0 1…

Solution

If m and &#963; 2 are the mean and variance of the random variable X . whose distribution is given by x 0 1…

Solution

If m and σ 2 are the mean and variance of the random variable X . whose distribution is given by x 0 1…