# Questions tagged [expected-value]

Questions about the expected value of a random variable.

4,756 questions
14 views

### Expectation and Variance of Infinite Sequence

We have an infinite sequence of independent variables where we take k labelled balls and put them into k labelled slots so that there is one ball per slot. We want to find the expected value and ...
15 views

### Does anything like expectation of joint distribution exist?

I know how to find the expectation of a function of a Random Variables, I was just wondering that does expectation of a joint distribution exists? I think, since expectation is an average which by ...
24 views

### Expected Value in joint probability distributions

I am very puzzled as to how they arrived at μ=2/5 in this example. I understand that μ is just expected value which would mean summing x or y with its possible realizations, but if x and y are max. 1, ...
36 views

### Expectation probability [on hold]

In a statistics examination, the mean score for 400 students is 78% and the standard deviation is 10%. How many students have scores (a) (i) more than 70 (ii) less than 90% (iii) between 70% and 90% ?...
46 views

### Hard expected value problem

Given a series of discrete random variables $Y_2, Y_3...Y_n$, such that for all $Y_i$ : $P(Y_i = e^i) = \frac{1}{i}$, $P(Y_i = 3) = \frac{1}{3}$, $P(Y_i = X) = \frac{2}{3} - \frac{1}{i}$, and $X$ ...
20 views

### Mathematical derivation of why Bagging reduces variance

I am having a problem understanding the following math in derivation that bagging reduces variance. The math is shown but can not work it out as some steps is missing. link
38 views

28 views

### Sucker Bet - Coin Flipping Stochastic Process

Having a lot of trouble working out this exercise. I have tried constructing the 8x8 matrix with all possible combinations of three flips of the coin {HHH, HHT, HTH, ... , TTT} and then calculating an ...
20 views

### Expectation of lost ball number

I have expectation problem that sounds like this: In the box we have 5 balls numbered U={2,2,2,3,3}. We lost one ball and we don't know which one. Then one ball was taken out from the box which ...
32 views

### 1st Yr Probability: what is wrong with my approach? (using indicator RVs)

Joe’s iPod has $500$ different songs, consisting of $50$ albums of $10$ songs each. He listens to $11$ random songs on his iPod, with all songs equally likely and chosen independently (so repetitions ...
23 views

34 views

### Conditional probability and expected value calculation

A football team, LIBO, wins a match with probability 0.75 irrespective of its opponents. What is the probability that the team wins 4 matches out of 5 matches? In a knockout tournament, LIBO ...
17 views

9 views

16 views

### Reference for EV/ betting game questions. [closed]

Need some good material to practice questions on probabilistic games. Mainly questions on the lines of finding EV and deciding whether it's a fair bet or not, or how much should one bet.
25 views

### Have I been rigorous in this simple argument with summation and expectation operators?

I am told that $A$ and $B$ are random variables, and that $\mathbf{E}(A|B) = \gamma B$. Define $D = A/B$. Using the law of iterated expectations it can be shown that $\mathbf{E}(D) = \gamma$. Now ...
58 views

41 views

### Expected value of mean plus the deviation from the mean

Suppose $r$ and $\theta$ are random variables with: $r = \bar{r} + \tilde{r}$ $\theta = \bar{\theta} + \tilde{\theta}$ where $\bar{r}, \bar{\theta}$ are the means, and $\tilde{r},\tilde{\theta}$ ...
A box contains $N$ tickets numbered $1, 2, 3,...., N$. If $m$ tickets are drawn one by one from the box without replacement, then find the mean of the sum of the numbers obtained on the tickets drawn. ...