0
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2answers
47 views

Solved - Use Random Number to Derive # based on Probability Table

Update I was able to derive the algorithm and implement it into excel. Thanks for the formula. Something like: ((z-xlbound)/d(x)*d(y))+ylbound See original sheet at end of post Original Post ...
1
vote
2answers
42 views

Expected Value of Identically distributed random variables

I have a very quick question regarding the expected value of two random variables $X,Y$ that are identically distributed and not necessarly independent. Is this equation valid? $E[XY]=E[X^2]$ If ...
0
votes
0answers
9 views

Is it possible to use multiple time scale algorithm here?

Suppose a random sequence is being generated (the next term generated depends on the previous term, but we don't know any distribution) until we hit some specific number. We want to calculate the ...
7
votes
5answers
650 views

Is the product of uniformly distributed numbers, uniformly distributed too?

My question is simple, I think. If we took two random natural numbers $a$ and $b$ uniformly distributed in a specific range $[c,d]$, is $ab$ a uniformly distributed too? What if $a$ and $b$ are not ...
2
votes
2answers
46 views

How to find out number of possible outcomes by trying over and over?

While working on my network exploration tool project, I've ran across the problem of reliably determining number of possible exit addresses of a tunnel with single entrance. I've came up with ...
0
votes
0answers
36 views

Is the probability of variable independence = 0?

I understand the concept of independence to be dichotomous- events are either independent or dependent. And while there are infinitely many ways for events to be dependent and only one way to be ...
1
vote
2answers
43 views

What is the expected value of this sum (drawing slips from a bag)?

Suppose there are thirteen slips in a bag, labelled 1-13. If I draw a 10, 11, 12, or 13 then I stop adding to the sum and return the sum. If not, I add the number I draw to the current sum and place ...
1
vote
1answer
20 views

Find the probability $P[ x(t) \le 1]$ where $x(t)$ is a filtered Poisson process (rect pulses)

I can't understand the following question: "The random process x(t) is defined as $$x(t) = \sum_{n=- \infty}^{+\infty} rect(\frac{t-\tau_{n}}{T}) \quad ,\quad t \ \epsilon \ (R)$$ where {$\tau_{n}$} ...
2
votes
1answer
29 views

The probability of getting a certain image by random pixelation

Well, seeing that I'm terribly bad at math I don't know how to solve this, I'll try to explain, excuse me if I sound dumb. Just suppose that I've got a photo/image with 320x240 resolution and 24 bit ...
31
votes
3answers
6k views

Making 400k random choices from 400k samples seems to always end up with 63% distinct choices, why?

I have a very simple simulation program, the sequence is: Create an array of 400k elements Use a PRNG to pick an index, and mark the element (repeat 400k times) Count number of marked elements. An ...
2
votes
0answers
58 views

Randomness in a sequence

For a function $f$ consider a random sequence $a_{n+1}$ can be either $a_n+f(a_n)$ or $a_n-f(a_n)$ Given that the next term in the sequence is subtracting $f(a_n)$ from the previous term 50% of the ...
0
votes
0answers
17 views

Spherical Sampling of Projected Disk

Given a 2D solid disk centered at some 3D point $\vec{x}$ with radius $r$ and normal $\vec{N}$, I need to compute a random unit vector from the origin that hits the disk. The vector needs to be ...
3
votes
1answer
72 views

[Probability]need help to understand the following expression

So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively. assume c is a constant. I am having huge trouble to understand the integration of the following ...
2
votes
2answers
37 views

Select an element without uniform distribution with a uniform random without iterations

I have N elements (numbered from 0 to N-1) and I must choose one but without the same probability. For example, I need that the 0 must happen 50% of times, 1 with a 25%, 2 with a 12.5%, etc. I don't ...
0
votes
0answers
83 views

Probability Question involving Probability Mass Function/Random Variables

Problem: When a paging system transmits a message, the probability that it will be received correctly by the appropriate pager is p. To ensure that the message is correctly received at least once, the ...
1
vote
1answer
22 views

Creating a bivariate distribution from two independent variables

If you have two random variables that are independent say $X\sim f_X (vars)$ and $Y \sim f_Y (vars)$. Is this a way to produce a bivariate distribution $f_{(X,Y)}$? $f_{(X,Y)} = p(X=x \cap Y=y) = ...
0
votes
2answers
42 views

Probability Random Variable question Need Help Please

You have a set of ten light bulbs - the lifetime of each of them being given by an exponential RV with mean 1000 hrs. Find the probability that.... (a) at least 7 of the bulbs function for 1500 or ...
0
votes
0answers
36 views

Proving properties of Random Graphs

I am asking the question on a slightly abstract level and it may depend on the specifics but it would be great to have related references or ideas. Consider the random graph model $G_{n,p}$ where its ...
3
votes
2answers
97 views

What is the probability of a specific sequence of 11 digits occurring in a random sequence of one billion digits?

This isn't homework, I'm actually (please don't ask me why) wondering how likely it is that any particular 11-digit telephone number will occur in the first billion digits of pi. My probability course ...
0
votes
0answers
42 views

Law of large numbers with random weights

Let $\mu_i$ be i.i.d. RVs with mean zero, and let $a_i$ be random weights that are not independent and are not identically distributed, $i=1,...,N$. $\mu_i$ is orthogonal to $a_j\;\forall j$. Is ...
1
vote
0answers
26 views

Random sampling and i.i.d.

Can you help me to clarify the following concepts by stating whether what I have written below is right or wrong? -random sampling: units are drawn from the population with a known probability of ...
2
votes
0answers
57 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 ...
1
vote
1answer
49 views

How does a pdf of the difference of two random variables relate to the pdf of each random variable

Let $T_1$ and $T_2$ be non-negative continuous random variables (rv) denoted in the form $T_i = \mu_i + \sigma_i X_i$ for $i=1,2$ where \begin{eqnarray*} T_{1} &=&\mu _{1}+\sigma _{1}X_{1} \\ ...
0
votes
0answers
12 views

Sampling a path in graph where each edge has a fitness

I'm writing an heuristic algorithm for the Travelling Salesman Problem. In one step, I have to generate a random path of length $n$ in a graph $G$. There is a real number in $[0, 1]$ associated to ...
1
vote
3answers
62 views

Convolution of maximum and minimum of uniform random variables

Let $X_1,\ldots, X_n$ be $n$ independent random variables uniformly distributed on $[0,1]$. Let be $Y=\min(X_i)$ and $Z=\max(X_i) $. Calculate the cdf of $(Y,Z)$ and verify $(Y,Z)$ has independent ...
3
votes
2answers
76 views

Alice and Bob card game

I came across this puzzle online in an online Princeton thingy (course?): Alice writes down two integers between 0 and 100 on two cards. Bob gets to select one of the two cards and see its value. ...
1
vote
0answers
35 views

Calculate expected value E(|x-y|^2)

I have two random variables (X and Y) that are uniformly distributed from 2.16 to 6.81 both. And I need to find E(|x-y|^2). Is this correct: ...
1
vote
2answers
45 views

Median of i.i.d. uniform random variables on the interval $[-1/2, 1/2]$

Let $X_1, X_2, \ldots , X_{999}$ be independent and identically distributed random variables on the interval $[-1/2, 1/2]$. Let $X_{500}$ be the empirical median; that is, $X_{500} = X_k$ for some ...
1
vote
0answers
14 views

Raffle between different groups composed by different numbers

I've got this issue, I need to prepare a raffle between teams for a cars race. Cars are grouped by teams. Rounds are 1:1, composed by different manches until the cars are done. Total number of cars is ...
0
votes
1answer
47 views

Random processes

I hope someone could tell me how to explain that "random process is continuous by probability" and "random process is differentiated by probability"? I know that definitions are these: Given a time ...
0
votes
1answer
196 views

Finding the expected value of the length of a minimal spanning tree of n randomly generated nodes bound in a box with edge length a.

Say we specify a number (n) of random points (x,y), bound within the axes and x=a, y=a. Given the number of points and the constraints on the boundaries, how can you calculate the expected value of ...
0
votes
2answers
52 views

Calculating the expected value of n randomly generated numbers?

Say I have a random number generator that will generate x numbers - not necessarily integers - on the continuous range between a and b. How can I calculate the expected values for these numbers? My ...
0
votes
0answers
28 views

Random noise and i.i.d's

In a book it is written that the quantity $\epsilon(\theta)$, called random noise, can be assumed to be i.i.d's when it does not depend on $\theta$. When it depends on $\theta$ it is said that the ...
0
votes
1answer
23 views

Am i in the right direction on this probability/random distribution question?

To improve the operation in the control tower of an airport, air traffic control engineers are assessing the delay due to taxi-out time, which is the duration between pushback and takeoff. suppose ...
1
vote
2answers
143 views

How to find binomial pmf with probability = another random variable

Assume that $Q$ is a random variable with density proportional to $q$ for $0 < q < 1$. Given $Q = q$, $N$ has a binomial distribution with parameters $n$ and $q$. What is the probability mass ...
1
vote
1answer
35 views

probility, placing balls, covariance

Can you please help to see where I did wrong? There are 10 balls, and each ball to be place in bin 1 and bin 2. Each ball is placed indepedently. Let X be the number of balls in bin 1 and Y be the ...
2
votes
1answer
33 views

probability, transformation on Random Variable

This is a more general question about the transformation of a random variable. Say X is given as a certain distribution, and Y=g(X). If it asks to compute the pdf of Y, I am having trouble to ...
2
votes
4answers
51 views

The Objectivity of Statistical Testing

I have a very generic question about applied statistics. Suppose, to make things simple, we have a biased coin with probability $p$ of landing heads. We want to determine if our coin is truly fair - ...
0
votes
0answers
58 views

probability, birthday paradox: need help to understand the solution

I need help to understand the following solution to a birthday paradox problem. problem:So you have $20$ people. Then let $P=$ # of pairs that share the common birthday. Compute ${\bf E}[P]$, ...
1
vote
2answers
85 views

Dice-Game with two-twenty sided dice.

EDIT: I'll give this another try, trying to be clearer. The game is played like this: Player A roles two-twenty-sided dice and multiplies the two integers together to get some integer, say x, with $ ...
0
votes
1answer
23 views

probability, depedence => uncorrelated?

One quick question. Two random variables are dependent, so it must be uncorrelated? Also for the terminalogy, does the term "uncorrelated" means two random variables have a corvariance factor of 0? ...
1
vote
1answer
22 views

probability, please help on bayes question

I dont need exact answer, I just need help to judge wether my following method is correct or not. Question:A physician has 5 patients. There are treatments A and B. Physician gives treament A to 3 ...
0
votes
1answer
23 views

probability, at least one is not present

you have $5$ red balls, $10$ green balls, and $15$ yellow balls in a balls. You randomly choose $5$ without replacement. What is the probability that at least one of the $3$ colors is not present ...
1
vote
1answer
34 views

probability, need help on the marginal densities

I need help on the marginal densities. In particular, I know you just integrate the joint pdf f(x,y) from y=-infinity to +infinity, but in the context of the below question, I have trouble to define ...
1
vote
1answer
85 views

probabilty, random variable independent

Let $X$ and $Y$ be independent Poisson random random variables with ($\lambda=1$). Are $X-Y$ and $X+Y$ independent? Justify My attempt: $X-Y$ => random variable is $0$. $X+Y$=> Poisson of ...
0
votes
2answers
39 views

probability, indicator random variable

Let $A,B,C$ be independent events with $P(A)=P(B)=P(C)=\dfrac{1}{2}$. Let $X$ be the indicator r.v. of the event $A \cup B$ and $Y$ the indicator r.v. of the event $B \cup C$. Compute ${\bf E}[XY]$. ...
0
votes
2answers
38 views

probability: arithmetic with random variables.

I have a question of using arithmetic on random variables. Please refer to the following question, to which I will present my solution using the arithmetic (which I thought it's correct but actually ...
1
vote
1answer
53 views

{Probability}: choosing keys from a pool without replacement

The OP is trying to understand the following question. The OP understand that if you can always write out the term $$P(X=k) \implies (1-\frac{1}{N})(1-\frac{1}{N-1})\cdots(1-\frac{1}{N-k+1}),$$ ...
0
votes
1answer
56 views

Probability: deviation from the mean

I am having trouble to understand the following. If $S_n=X_1+X_2+......+X_n$, where X_1,X_2 are Bernouli (p). I don't understand this. So you get an intermediate point Constant* sqrt(n). To the ...
0
votes
1answer
34 views

Random sample and probability

A random sample of 325 new toothbrushes showed that 14 were defective. What is the estimate of the probability that a new toothbrush is not defective? Either a toothbrush is defective or not. What is ...