Calculate the expected value and variance of $x$ , if $x$ denotes the number obtained on the uppermost face when a fair die is thrown.

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Solution

Let $x$ denote the number on the uppermost face of the dice.
And the probability of any number on the uppermost face is $1 / 6$
when $x = 1 P (1) = 1 / 6$
$x = 2 P (2) = 1 / 6$
$x = 3 P (3) = 1 / 6$
$x = 4 P (4) = 1 / 6$
$x = 5 P (5) = 1 / 6$
$x = 6 P (6) = 1 / 6$
Hence adding all we get mean as $6 / 6$

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Calculate the expected value and variance of x, if x denotes the number obtained on the uppermost face when a fair die is thrown.

Let x denote the number on the uppermost face of the dice.And the probability of any number on the uppermost face is 1/6when x=1P(1)=1/6 x=2P(2)=1/6 x=3P(3)=1/6 x=4P(4)=1/6 x=5P(5)=1/6 x=6P(6)=1/6Hence adding all we get mean as 6/6

Calculate the expected value and variance of $x$ , if $x$ denotes the number obtained on the uppermost face when a fair die is thrown.