Question

The conditional variance of X, given Y, is defined by Var(X|Y) = E[(X - E[X|Y])$^2$|Y] Prove the conditional variance formula, namely, Var(X) = E[Var(X|Y)] + Var(E[X|Y]). Use this to obtain Var(X) in Example 1 5(B) and check your result by differentiating the generating function

          The conditional variance of X, given Y, is defined by
Var(X|Y) = E[(X - E[X|Y])$^2$|Y]
Prove the conditional variance formula, namely,
Var(X) = E[Var(X|Y)] + Var(E[X|Y]).
Use this to obtain Var(X) in Example 1 5(B) and check your result by
differentiating the generating function

The conditional variance of X, given Y, is defined by
Var(X|Y) = E[(X - E[X|Y])^2|Y]
Prove the conditional variance formula, namely,
Var(X) = E[Var(X|Y)] + Var(E[X|Y]).
Use this to obtain Var(X) in Example 1 5(B) and check your result by
differentiating the generating function

Added by Felipe R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Manisha Sarker

Step 1

First, we need to prove the conditional variance formula: Var(X| Y) = E[(X - E[X| Y])^2| Y] = E[X^2 - 2XE[X| Y] + E[X| Y]^2| Y] = E[X^2| Y] - 2E[XE[X| Y]| Y] + E[E[X| Y]^2| Y] = E[X^2| Y] - 2E[X| Y]E[E[X| Y]| Y] + E[E[X| Y]^2| Y] = E[X^2| Y] - E[E[X| Y]^2| Show more…

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The conditional variance of X, given Y, is defined by Var(X| Y) = E[(X - E[X| Y])^2 | Y]. Prove the conditional variance formula, namely, Var(X) = E[Var(X| Y)] + Var(E[X| Y]). Use this to obtain Var(X) in Example 1 S(B) and check your result by differentiating the generating function.