Question: Roll two dice and define the random variable X to be the sum. (a) Calculate its mean E[X] and variance E[(X E[X]) 2 ].
Roll two dice and define the random variable X to be the sum.
(a) Calculate its mean E[X] and variance E[(X − E[X])2].
(b) Compute E[X2] and show that the variance E[(X − E[X])2 ] = E[X2 ] − (E[X])2 .
2. Show that, for any random variable X, E[(X − E[X])2 ] = E[X2 ] − (E[X])2 .
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