(a)[1]
Demonstrate that $\operatorname{Var}(X) = 2$.
(b)[4]
Fiona owns a second spinner, again with five sides numbered $1, 2, 3, 4, 5$. She thinks that it is biased so that the expected score is below $3$. To test this idea, she intends to spin it $40$ times. If the mean score is less than $2.6$ she will decide that her spinner is biased in this way. Find the probability of a Type I error.
(c)[1]
State the meaning of a Type II error in this context.