(a) Let ( x ∼ UD(1,n) ). Prove the following relations:
[ E(x) = n+1/2 ]
and
[ Var(x) = (n-1)²/12 ]
(b) Let ( x ∼ UC(a,b) ). Prove the following relations:
[ E(x) = a+b/2 ]
and
[ Var(x) = (b-a)²/12 ]
Which of the following distributions is characterized by a Uniform Distribution?
a) Throwing a fair die
b) Selecting a card from a deck of shuffled cards
c) Measuring the weight of apples in a basket
d) Tossing a biased coin