Part A:
Here,
P(i) = 1/6
For all i = 1, 2, 3, ... 6,
E[X] = 1*(1/6) + 2*(1/6) + 3*(1/6) + 4*(1/6) + 5*(1/6) + 6*(1/6)
= 7/2 or 3.5
Now,
E[X2] = Σ i2*P(X=i) (to a total of 6, starting from 1)
Here, i = 1, 2, 3, ... 6,
Or, E[X2] = 1/6 + 22/6 + 32/6 + 42/6 + 52/6 + 62/6
Or, E[X2] = 91/6
Now, Var(X) = E[X2] - (E[X])2
= 91/6 - (7/2)2
= 35/12
Part B:
Please find the solution below:
End of the Solution...
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