0
votes
2answers
25 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
31 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
50 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
28 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 ...
110
votes
23answers
9k views

Is an SD card a fair coin… to me?

This morning, I wanted to flip a coin to make a decision but no coins were in reach. There was however an SD card on my desk: Given that I don't know the bias of this SD card, would flipping it be ...
0
votes
0answers
15 views

Probability in a weighted Random

This is actually a question that came up whilst programming, but i figured this is more a question for the mathematicans: in a database have a set of roughly 500 entries. now i want to get 10 random ...
0
votes
1answer
33 views

Given the distribution of a random variable $R$, who do you get a uniform random variable $U$?

Let us say you have a random variable $R$. How would one generate a uniform random variable $U$, with the maximum possible entropy (or infinite entropy, if $R$ has such)? (For simplicity, you may ...
0
votes
1answer
19 views

Density on the square, expected value

Let $f: [0,1]^2 \rightarrow \Bbb R^{+}$ a density function on the square. I suppose that the random variable $X=(X_1,X_2)$ has the density f with respect to the lebesgue measure. I denote ...
0
votes
1answer
29 views

Moments of Geometric Random Variable

Let $X$ be a geometric random variable i.e. it represents the number of consecutive failures before you get the first success where the success probability is $\rho$. We know $E[X] = 1/\rho$ and ...
4
votes
0answers
122 views

Asymptotics of sum of binomial distributions

Definition 1: For any random variable $X$, we define $Bin(p,X)$ as a variable with binomial distribution having parameters $p$ and $X$. Definition 2: For all $i \in \mathbb{N}$, define recursively ...
1
vote
1answer
84 views

Solution of equation of binomial random variables

Is it possible to find the probability distribution of the random variable $X$ that solves the following equation? $$ X = Bin(X, p) + Bin(X, 1-p), $$ where $Bin(X,p)$ is a random variable distributed ...
0
votes
0answers
24 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 ...
0
votes
1answer
23 views

Probability of occurrence after Latin Hypercube sampling and then random sampling

I am using Latin Hypercube sampling to obtain numbers from a Normally Distributed set of data, so that I get a uniform spread of numbers across the Normal Distribution. I then select a number at ...
1
vote
1answer
37 views

Probability of random variable in Normal Distribution

I've been talking to my lecturer about choosing random values from a Normal Distribution and he says the following: "Roughly 68% of expected values $ \in (\mu-\sigma,\mu + \sigma)$ does not imply ...
2
votes
1answer
36 views

Probability question (grid)

Say I have a grid of 10x7. Every square of that grid is empty. Then, 20 squares, chosen at random, are filled (a square can only be filled once, so no duplicates allowed). What is the probability of ...
2
votes
3answers
75 views

Probability of collecting all 5 different items at random with different weights

There are 5 different items in a set, each with a weighted chance of being rolled randomly [A-E]. The weights add up to 100%. $$A=5\%, B=10\%, C=15\%, D=30\%, E=40\%$$ You get 1 item every roll no ...
0
votes
1answer
25 views

Generating Random Serialnumber with least similarity

I want to generate 16-digits hexadecimal serial-number like: F204-8BE2-17A2-CFF3. (This pattern give me 16^16 distinct serial-number But I don't need all of them as I describe below) I need an idea ...
0
votes
2answers
46 views

the maximum of two random variable

The maximum of two random varibles $X$ and $Y$ is: $$Z=\max\{X,Y\}= \begin{cases} X & \text{if } X \geq Y \\ Y & \text{if } Y \geq X \end{cases}$$ I don't understand. So if I roll two dice, ...
3
votes
0answers
34 views

Can I solve this probabilistic problem or do I need more data?

This problem happened to me almost 3 years ago and I just discovered this site by luck, so I want some help to know if this problem is solvable (if so, I would like to know how to solve it as well as ...
0
votes
2answers
35 views

Distribute a population size based on fractions using random number generator drand48()

I have a population size of say 5000 people. Every person belongs to either A, B, C or D category. I want to split the population as per a given fraction provided by user. for example, 99% of A, 0.4% ...
0
votes
1answer
17 views

Looking for a random statistical biaised function

A common random function is designed like a dice, if you call it many times it will yield approximately the same number of times 1, 2, 3, 4, 5 and 6. Statistically, you could say it's equally spread ...
0
votes
0answers
45 views

Derive c.d.f and p.d.f of a random variable which is defined as function of two random variable

Let $x_1$ and $x_2$ are independent random variable with p.d.f $f(x_1)$ and $f(x_2)$. How to derive c.d.f and p.d.f of random variable $y$, which $y = \frac{x_1 x_2}{ax_1 x_2 + bx_1 + cx_2 + d}$ ...
0
votes
1answer
44 views

2 dimensional random walk - hit of targets

Consider a random walk in $\mathbb{Z}^2$, $x(j) = x(j-1) + \xi_j$, where the increments are random variables independent and identically distributed with finite support, the expectation $m := ...
0
votes
1answer
44 views

random walk with dependent increment

Consider the following sort of random walk. The position of the walker at time $t$ is represented by the random variable $r(t)$, with $r(0) = 0$. The variable satisfies the following equation, $$ ...
28
votes
3answers
4k views

Why does this not seem to be random?

I was running a procedure to be like one of those games were people try to guess a number between 1 and 100 where there are 100 people guessing.I then averaged how many different guesses there are. ...
4
votes
3answers
134 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
1answer
77 views

What is the expected error of a randomly generated number?

Forgive me if this question is unclear, as I'm not a mathematician. The question has come up in an industrial sensor application. I am trying to make the displayed sensor value to be more steady ...
4
votes
3answers
181 views

Probability that a chosen number will be a Fibonacci number

Suppose that I randomly choose an integer $x$ with $1 \leq x \leq n$ where $n$ is a natural number. What is the probability that $x$ will be a Fibonacci number?
0
votes
0answers
17 views

Reciprocal antiderivative of a process in an expected value

Given a stochastic process $X=\left \{ X_{t}:t\in [0,T] \right \}$, with known probability and spectral density function, is there a way to calculate or estimate the following expectation: $$\left ...
2
votes
1answer
83 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 ...
0
votes
1answer
63 views

Probability randomly picked card is smaller than another picked card

Given a set of m cards that have values pairwise different with range 1 to m, what is the probability that after shuffling the card, and picking two of them, the first one is larger than the second ...
3
votes
1answer
38 views

Find probability of a Poission process.

Given that $N=\{N(t)\mid t\geq 0\}$ is a Poisson process with parameter $\lambda>0$ I need to find $P(N(3)=2\mid N(1)=0, N(5)=4)$ So this is a conditional probability (can anyone clarify if this ...
1
vote
0answers
71 views

Randomized packing of items

An adversary gives you a set of items whose total size is $x$ (he gets to choose how $x$ is distributed. e.g. there may be $k-1$ items of size $\frac{x}{k}$ and 2 items of size $\frac{x}{2k}$). The ...
0
votes
1answer
56 views

Frequency analysis/discrete uniform distribution in multiple choice tests

I may be using the wrong terms in the title but I read that if something is random then each character will occur an equal amounts of times. I read this when reading about the One-Time Pad cipher, ...
0
votes
2answers
63 views

Addition of probabilities and gambler's fallacy

Say you have a 1 in 6 chance of winning a card game. The more times you play, the higher the odds of you winning. $$P(\text{win over 1 trial}) = 1/6 \\ P(\text{win over 2 trials}) = 1/6 + 1/6 \\ ... ...
2
votes
1answer
63 views

Probability that number begins with one

I have three very similar algorithms generating very different results. In all of them I'm calculating distribution of first number of random number. First algorithm Here I'm generating random ...
0
votes
2answers
42 views

What is the statistical difference (if any) between these two methods of generating an n-digit random number?

To preface, this question is coming from a software developer so it's written from that perspective. If I need to generate a random number with $n$ digits, I could do it in one of two ways. a. Ask a ...
1
vote
1answer
27 views

How many iterations does it take to cover a range with random values?

Let's say I have a random number generator that generates integers uniformly from 0 to n-1 (where n is some positive integer). What is the expected number of iterations after which all the values ...
2
votes
1answer
49 views

Independent sequences

Let $\{x_i\}_{i = 1, ...,n}$ , $\{y_i\}_{i = 1, ...,n}$ be sequences generated by a pseudo-random number generator using different seed keys, for example $ x_0$ and $y_0$. Are $\{x_i\}$ and $\{y_i\}$ ...
1
vote
0answers
23 views

Reservoir sampling - understanding probabilites

I am reading about reservoir sampling(method for selecting random sample out of some data), but cannot understand a few things about probability I came across. The article at blog, says that if I'm ...
1
vote
0answers
52 views

Packing a larger sphere with smaller spheres in high dimensions

We were discussing today the probability of leaving a point uncovered while trying to fill a larger sphere by randomly throwing in smaller spheres. Here's the argument: We are working in ...
1
vote
2answers
68 views

Find the probability of two random real numbers $x$ and $y$ between $0$ and $2$, where $\min(x,y) < 2/3$

Here is a picture of what I did so far. http://sdrv.ms/HhxIvu I got a result of $\frac59$, because the total area is $4$, and I'm subtracting the square with side of $\frac43$. Can anyone confirm ...
1
vote
1answer
81 views

Searching for random items in a set of lists

This is a programming question, but I'm interested in the math behind it so I think it's better asked here. Say I have a list of items and I'm looking for one item in the list that satisfies a ...
1
vote
1answer
56 views

probability of sequence of random variables

We're going to look at a random process, which is a sequence of random variables that depends on time. Let $X(t)$ = $A/t$ where A has the density $f_A(a)$ = $3/8$ $a^2$ for $ 0<=a <= 2$. Assume ...
1
vote
1answer
871 views

Probability density of Continuous uniform distribution over the unit circle

If we want to chose a point $(x,y)$ uniformly at random from a unit circle in a plane, why is the joint probability density of the random variable $f(x,y) = \frac{1}{\pi}$ for $x^2+y^2\leq1$? The ...
1
vote
1answer
200 views

problem on random variable in probability

A game consists of first rolling an ordinary 6-sided die once and then tossing a fair coin once. The score, which consist of adding the number of spots showing on the die to the number of heads ...
1
vote
2answers
286 views

Creating Custom Random Number Generator

My statistics are rusty, but here's what I'm trying to do. Creating an application around football and have this distribution around rushing yards per attempt. ...
2
votes
3answers
369 views

Random number generator with discrete probability distribution

Is there a general algorithm for implementing a PRNG with a probability distribution?
0
votes
1answer
49 views

Probability of random vector lying on a hyperplane

I have a random vector $v \in \mathbb R^n$, of which the elements are independent. Now there is also a hyperplane $S \subseteq \mathbb R^n$ of dimension $n-1$. The vector is drawn from any continuous ...
2
votes
1answer
174 views

Average number of bins occupied when throwing $n$ balls into $N$ bins

There are $n$ balls and $N$ bins. At each time, a ball is thrown in one bin of $N$ bins at random. This repeats n times. So that in total $n$ balls are thrown into bins. The question is, on average, ...