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Results tagged with expected-value
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user 362295
The expected value of a random variable is a weighted average of all possible values a random variable can take on, with the weights equal to the probability of taking on that value.
2
votes
1
answer
196
views
Prove E[Y|X] = f(X)
I have a model $Y = f(X) + \epsilon$
where $\epsilon$ is independent of $X$ and $\mathbb{E}[\epsilon]=0, \mathbb{E}\left[\epsilon^2\right]=\sigma^2$.
Show that
$$
f(X)=\mathbb{E}[Y \mid X]
$$
This is …
- 25
0
votes
0
answers
51
views
Derive E[Y|X] when the joint probability is given
Now, consider joint density of $X, Y$ :
$$
f_{X, Y}(x, y)=\left\{\begin{array}{l}
\frac{1}{\pi} ; X^2+Y^2<1 \\
0 ; \text { Otherwise }
\end{array}\right.
$$
Derive $E(Y \mid X)$.
I know how to calcula …
- 25