# Tagged Questions

A conditional expectation is the expectation of a random variable, given information on another variable or variables (mostly, by specifying their value).

27 views

40 views

39 views

44 views

### Expectation of a conditional density

I'm trying to figure out why the following equation holds: $$f_{Y}(y) = E(f_{Y|X}(y|X))$$ I have sort of "worked out" the RHS to be: \begin{align} f_{Y}(y) &= E(f_{Y|X}(y|X)) \\[5pt] &...
91 views

### Conditional Mean in Linear Regression

I have a question about linear regression in general. Suppose we have the following Data Generating Process:$$y_{i}=x_{i}\beta+\epsilon_{i}$$ Now, the thing is that from my understanding, each ...
15 views

### Deducing the regression function using the Squared Error Loss Function [duplicate]

I am reading Elements of Statistical Learning, and came across a deduction which I cannot understand. In the second chapter, the author defines the squared error loss and deduces the conditional ...
83 views

### Can I apply statistics to catch rare diseases or make decisions about fate?

Suppose I am 50 years old and a study found that in my city 10 people (CI=4 people) die at 50. Now it's July and I have a very malignant disseminated cancer and this year 14 people died at age 50 in ...
55 views

### Conditional Expectation of sum of uniform random variables?

Let $X,Y$ be independent uniform random variables on interval $[0,1]$. Can someone show me how to find the expectation of $X$ conditioned on $X+Y \ge (\text{say}) 1.3$? $$E[X | (X+Y) \ge 1.3]$$ ...
53 views

### X is stochastically increasing in Y $\implies$ $E\left[Y| X\right]$ increasing in X

I have two random variables, $X$ and $Y$. I know: $\text{pr}\left(X \le u | Y\right)$ is a decreasing function of $Y$ for all $u$. Does this imply that: $\mathbb{E}\left[Y | X\right]$ is increasing ...
### With given numbers $a_1, a_2,a_3,…,a_N$, let $W=\Sigma_{i \in s_n}a_i$. Calculate the mean and variance of $W$
From the set $R=\{1,2,3,...,N \}$, a set $s_n$ of $n$ numbers are chosen without replacement, $0<n<N$. With given numbers $a_1, a_2,a_3,...,a_N$, let $W=\Sigma_{i \in s_n}a_i$. Calculate the ...