Questions tagged [expected-value]
Questions about the expected value of a random variable.
6,896
questions
0
votes
0
answers
15
views
Bound on the expectation of the maximum of a sequence, given bounds on the expected value of each element.
I have a sequence of independent random variables $U_1, U_2, \dots,U_N$.
Suppose $\mathbb{E}[U_i] \leq 1$ for all $i=1,\dots,N$, and let:
$$M_N = \max_{i=1,\dots,N} U_i$$
It is easy to see that $\...
- 21
2
votes
2
answers
75
views
Optimal strategy for uniform distribution probability game
There are 2 players, Adam and Eve, playing a game. The rules are as follows: $n$ and $d$ are chosen randomly. Adam samples a value $v$, distributed uniformly on $[0,n]$, and can either cash out $v$ or ...
- 21
0
votes
1
answer
21
views
dividing the determinant of a matrix by the expected value of the determinant of the same matrix over a uniform distribution
Let $A, B$ be square $n \times n$ matrices as follows:
$$
A = \begin{bmatrix}
x_1&x_2&\cdots&x_n\\
x_{n+1}&x_{n+2}&\cdots&x_{2n}\\
\vdots&\vdots&\vdots&\vdots\...
- 451
7
votes
3
answers
876
views
This expected value has a minimum!
Problem. Let $X$ be a positive, real random variable whose probability density function is bounded by $1$. Prove that $E[X]\geq \frac 12$.
Hi everyone. This problem is essentially saying that the ...
- 984
-1
votes
1
answer
28
views
Probability - Find the expected number of item throws into N containers until one of the container reaches k items [closed]
There are $N$ empty containers, which are unlabeled and are exactly the same. Each time, with equal probability, a ball is throwed into a random container.
Q: What is the expected number of throws $f(...
- 11
0
votes
1
answer
69
views
What is the uses of Expected Value in this context?
I'm reading The Element of statistical learning: https://hastie.su.domains/ElemStatLearn/ and having question regarding this example on pages 23 and 24:
"Suppose we have 1000 training examples $...
1
vote
1
answer
53
views
Conditional expectation - alternative expression
Consider the following set-up.
$F:[0,\omega]\rightarrow[0,1]$ where $X$ is a real-valued random variable.
The conditional expectation of $X$ given $X<x$ is:
$E(X|X<x)=\frac{1}{F(x)} \int_0^s tf(...
- 1,467
1
vote
1
answer
38
views
Doubts on "An Intensive Introduction to Cryptography" exercise about Shannon's entropy
I was going through the exercises in An Intensive Introduction to Cryptography (see full PDF here), and in particular, I had some doubts on Exercise 0.12 (found on page 42). Here is the relevant ...
- 158
1
vote
0
answers
21
views
Upper bound for distribution function for variable with zero expectation. [duplicate]
A problem from final Year 1 probability exam.
Is it true for any random variable $Y$ s.t. $E[Y]=0$ and $E[Y^2]<\infty$ that:
$P(Y>x)\leq\frac{E[Y^2]}{E[Y^2]+x}$ ?
I thought we can rewrite it ...
- 124
4
votes
1
answer
72
views
Expected Number of Letters Typed Until MOO is Typed When Letters Are Typed Randomly
I'm failing to see the mistake in my reasoning for this problem. Here is the problem:
Problem
A man can only type two letters: M and O. He types M with probability $.4$ and types O with probability $....
- 138
0
votes
1
answer
30
views
Question on the expected number of same color balls left in a urn
I'm working on a problem where I am given an urn with $a$ white balls and $b$ black balls. One ball at a time is selected randomly until there is only balls of the same color. I am asked to find the ...
- 115
3
votes
0
answers
37
views
$L_2$ convergence of bivariate function
I have the following problem:
Let $X,Y$ be random variables with distributions $P_X,P_Y$ and $f_0$ be a map from the support of X,Y to the reals. I define a new function $\chi_0(y) = E_X[f_0(X,y)]$. ...
- 33
3
votes
0
answers
77
views
+50
Expected number of closed shapes in an $n\times n$ grid with some lines missing
I came up with a math puzzle that I can't figure out how to solve. I feel like it has enough "math" to make it more appropriate to post here than to the Puzzling Stack Exchange. Here it is (...
- 1,688
0
votes
0
answers
19
views
Which distributions have nice closed form expressions for expected value of exponential?
which distributions have nice closed form expressions for
$e^{-kx}$ and $xe^{-kx}$, where $k$ is some known constant? Ideally the support of the distribution should be positive, so for example the ...
3
votes
0
answers
55
views
Expected number of edges to draw in a bipartite graph until you get a crossing
I was asked by a friend to calculate the number of edge crossings in a $m \times n$ complete bipartite graph:
Now play a game where you randomly select an edge with equal probability each turn: what ...
- 141