Solution Found!
If Y is a continuous random variable such that E[(Y ?a)2]
Chapter 4, Problem 35E(choose chapter or problem)
QUESTION:
Problem 35E
If Y is a continuous random variable such that E[(Y −a)2] < ∞ for all a, show that E[(Y −a)2] is minimized when a = E(Y ). [Hint: E[(Y − a)2] = E({[Y − E(Y )] + [E(Y ) − a]}2).]
Questions & Answers
QUESTION:
Problem 35E
If Y is a continuous random variable such that E[(Y −a)2] < ∞ for all a, show that E[(Y −a)2] is minimized when a = E(Y ). [Hint: E[(Y − a)2] = E({[Y − E(Y )] + [E(Y ) − a]}2).]
ANSWER:
Answer:
Step 1 of 1:
Suppose that such that
for all
we need to show that
is minimized when
We know the mean of any random variable is same as the expectation.
Hence we can write,
……….(1)
(add and subtract