2
votes
0answers
52 views

“Alice and Bob” problem with matrices

Alice has a binary matrix $A$, and Bob has a binary matrix $B$. Both matrices are of size $n \times n$. Alice and Bob want to check if the matrices are equal except for exactly $1$ entry. Alice has to ...
0
votes
0answers
29 views

Random sample taken, what is probability?

It was determined that 22% of all stock investors are retired people. In addition, 38% of all U.S. adults invest in mutual funds. Suppose a random sample of 20 stock investors is taken. a. What is ...
1
vote
2answers
19 views

Show that $Cov(X,Y) \geq -23$

if $X,Y$ are two random variables and: $Var(X) = Var( Y) = 23$ how can i show that $Cov(X,Y)\geq -23$ can someone give me some hints on how to show it?(not an answer) i know that $Cov(X,Y) = E(XY) ...
4
votes
3answers
157 views

Recursion with Random number?

function foo(n) if n = 1 then return 1 else return foo(rand(1, n)) end if end function If ...
1
vote
0answers
44 views

Probability of random functions where domain equals co-domain

Given random function defined by $f: [n] \rightarrow [n]$, chosen uniformly, what is probability that the function is injective, surjective, or bijective? If $[n]$ is a set of discrete elements, ...
2
votes
1answer
88 views

Probability of picked cards to be smaller than the largest picked card

I have an assignment for my algorithms module that requires us, amongst other things, to find the equations for the following question. Edit - Question Updated You have n cards with pairwise ...
6
votes
1answer
1k views

The parking problem riddle

Assume a street of 300 meters, that you can park your car alongside the pavement. Assume that there is a big parking problem in the area. Assume that the pavement is continuous, without interruptions, ...
2
votes
2answers
301 views

Statistics Probability Help

I just began to take this stats course in HS and I'm a little stuck on these 2 problems below. Can anybody please help me out with the solutions? Thank you. Anything is appreciated. Let $Y$ be a ...
1
vote
1answer
197 views

Expected number of tosses - coin tossing

I have here 2 methods for generating a random number, and I need to calculate the expected number of tosses for each method. In each, we let n = log(N) Ne be the bit-length of N and let ...
0
votes
1answer
124 views

Inner product of two vectors with Rademacher random entries

I am lost with the signs cancellation. Please help me to calculate this inner pruduct. Let $a$ and $b$ be two $2m$ dimentional vectors such that their entries are Rademacher random variables and ...
2
votes
1answer
89 views

$\chi^2$ test and sampling variance

Let $f(x)$ denote the pdf of a $\chi^2$-distribution with $n\in\mathbb{N}$ degrees of freedom given by $$f(x) = \frac{2^{-n/2}}{\Gamma(n/2)}\cdot x^{n/2-1}\cdot\mathrm ...
2
votes
2answers
43 views

Transformation of first moment

We consider a multiple-choice test with exactly three yes/no-questions. The following rating scheme is given: correct answer +1 point, wrong/missing answer -0.5 points - a negative result is NOT ...
4
votes
0answers
622 views

Random graph connectivity, and the existence of isolated vertices

Here $G_{n,p}$ represents the Erdős-Rényi random graph model, where the graph has order $n$ and each edge is added independently with probability $p$. I am faced with proving the following claim: ...
13
votes
3answers
1k views

choose a random number between 0 and 1 and record its value. and keep doing it until the sum of the numbers exceeds 1. how many tries?

choose a random number between 0 and 1 and record its value. Do this again and add the second number to the first number. Keep doing this until the sum of the numbers exceeds 1. What's the expected ...
3
votes
0answers
177 views

Simulation and Stochastic Processes

Supposing we want to take a sample from the distribution $p(x)=cp^*(x)$ where $c$ is the normalization constant and $p^*(x)$ is given by $$p^*(x)=0.5\exp(-(x-\mu_1)^2)+0.5\exp(-(x-\mu_2)^2).$$ ...
3
votes
1answer
1k views

Expected value in collecting a set of coupons

There are $k$ types of coupons. Independently of the types of previously collected coupons, each new coupon collected is of type $i$ with probability $p_i$ s.t. $\sum\limits_ {i=1}^kp_i =1$. If $n$ ...
1
vote
1answer
92 views

Help understanding conditional probability

Hi I'm having a hard time wrapping my head around this particular problem. Suppose the lifetime of a shirt bought from Sears, in days, is a non-negative random variable $L$ with probability mass ...
0
votes
2answers
866 views

Calculate the probability of a simple event

I'm beginning to study probability and an exercise in the study guide that asks me to calculate: What is the probability that the month January, of one year randomly selected have only four Sundays? ...
0
votes
1answer
100 views

why the increment doesnt affect the randomness?

I'm doing some homework and I need to answer why the increment (b) doesn't affect randomness in the mixed congruential method. The formula is $$X_{n+1} \equiv (a X_n + b) \mod m$$
1
vote
1answer
600 views

Doubt in Discrete-Event System Simulation by Jerry Banks,4th Edition

I'm new to the Math forum here, so pardon my question if it seems juvenile to some. I've googled intensively,gone through wikipedia,wolfram and after hitting dead ends everywhere have resorted to this ...