6. Find the variance of a random variable ‘X’ whose value when two dice are rolled is X[(i,j)]=2i, where ‘i’ is the number on the first die and ‘j’ is the number on the second die.
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p(X = k) is 1/6 for k =2,4,6,8,10,12 and is 0 otherwise,
E(X)= (2+4+6+8+10+12)/6=7,
and
E(X^2) = (22 +42 +62 +82 +102 +122)/6=182/3.
It follows from Theorem that V (X)= E(X2)−E(X)2 =182/3−49=35/3.
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