Random Definition and 1000 Threads

Homework Statement [1] A random variable X is distributed as fX(x) = 1/9*(1+x)^2 1{-1<= x<= 2}. a) Find the density function of Y = -X^2 + X + 2. b) Find the cummulative distribution function of Y = X1{-1<=X<=1} + 1{X>=1} [2] Find the function that transforms a variable X with fX(x) =...

If a discrete random process can be viewed as a collection of random variables indexed by a value n and a discrete N dimensional random variable can be viewed as N random variables with with a joint pmf. In these cases it seems like there is not much difference between a N dimensional random...

Hi, I recently read an article on random matrix theory at newscientist.com and my interest is quite peaked. I was wondering if anybody taken a class on this and would kindly recommend a text on it. I have taken linear algebra but I have not taken anything beyond that. So also is there any...

I have a problem concerning a one-dimensional random walk in potentials. Assume a one-dimensional space [0,1] and a probability distribution p(x). At every point x we have a probability p(x) to go left and 1-p(x) to go right. Assume some smooth distribution of p(x) with boundaries p(0) = 0 and...

I'm sitting here with an interesting problem that I can't seem to figure out. I'm given two random variables X=a*exp(j*phi) Y=b where both a and b are known constants. phi is uniformly distributed on the interval [0,2pi) a third random variable Z=X+Y. My goal, is to find the...

What's the value of a random variable?

Homework Statement Suppose we want to estimate a binomial proportion, p. We take a sample of size n and count X successes. Consider a Bernoulli random variable, Y that is 1 with probability p and 0 otherwise. Show that the mean and variance of Y are p and p(1-p), respectively...

Can someone give me a little test problem? An easy one please, I'm new to this lol. Make the method random, so I have to try all three. Sub,Fac,Conj

Hello my question is stated below: Task 3: Determine the probability that a random variable (X) having a normal distribution with μ = 20.15 and σ = 6.27 minutes will take on a value less than 9.5. I've tried this: Standardised score = (9.6-20.15)/6.27 = -1.698 Now i don't know how...

I've been experimenting with a hardware random number generator. My circuit amplifies transistor noise and converts it to a digital output. My program (.Net) reads the output into an array of double precision values. My voltages range from -7 to 7 (well within the range of my ADC) and have 16...

Hi, I've been working on this problem but I feel like I'm over complicating it. If you have a random variable X= a*e(j*phi), where phi is uniform on the interval [0,2pi) and a is some constant, and another random variable Y= b where b is a constant. I'm looking to find the probability density...

Homework Statement For the random variable X with the following cumulative distribution function: Calculate P(X\leq1.5|X<2), P(X\leq1.5|X\leq2) and P(X = -2| |X|=2) The Attempt at a Solution This is an exercise about a subject I'm yet to see in class, but the teacher asked us to...

Hello everyone I'm new to these forums, I'm not from an English speaking country so I'll try to explain my self as clearly as possible. I have a question that has been troubling me for quite a while. Are there any fundamentally random occurrences in physics? in other words, Is there a...

How can we say that evolution is random when it is based on choice aswell? For example the first creatures that came onto land made a choice to do so. Sure they were probably pushed there to survive but they still made the choice. Throught out evolution these decisions were made and evolution...

Suppose we have a random number generator which gives a random numbers from a set {1,2,3,...,N}, and any single number of these comes out with probability 1/N. Then fix some number M > N, and take M random numbers out from the generator. What is the probability, that these M numbers include...

Hi all, I was wondering whether there was any work done on a random walker on a 1D lattice with diffusing boundaries? Any links or suggestions would be great!

Homework Statement Ten cards are face down in a row on a table. Exactly one of them is an ace. You turn the cards over oen at a time, moving from left to right. Let X be the random variable for the number of cards turned before the ace is turned over. What is the probability function for...

I am a little fuzzy on the meaning of Independent Identically distributed random variables. I understand the independent part but still not 100% on the identically distributed part. I understand that identically distributed means they have the same pdf and cdf but does this mean that they have...

How do i randomize a position on a sphere? Using a random number between 0 and 360 for longitude and a number between -90 to 90 for latitude would make it more probable to get closer to the poles right?

Homework Statement Let X and Y be two independent random variables each exponentially distributed with parameter 1. Define a new random variable: z = \frac{x}{{x + y}} Find the PDF of Z Homework Equations The Attempt at a Solution \begin{array}{l} {F_Z}(z) = P(Z < z) =...

i am writing a MATLAB m file. i need to generate a NxN matrix 25% filled with 0s and 1s in a random pattern... is this at all possible? also, in an NxN matrix, i need to select a 3x3 matrix centered around a certain point, can you help me out with this? many thanks for your help

Hello; I remember being taught long ago that radioactive decay is random, but, no one ever explained to me why. Surely there has to be a reason for it? Or is it simply the case of it not being random? (particles in gases don't move randomly, it is dependent on various factors) Thanks.

I have the intrinsic noise PSD spec for Honeywell's QA3000 accels, and I need to find the velocity random walk due to noise to show that I'm within my allowable. The PSD is given in units of g^2/Hz vs Hz. I'm given a velocity random walk due to noise spec of 15 (micro-m/s)/rt(s) that I must be...

I have been busy trying to generate, using FORTRAN's random number generator, random x and y co-ordinates which follow a simple pattern such as x2-100x, but for some reason the FORTRAN compiler prints nothing. Anybody want to help me with this problem? program quadraticdistribution...

Hello, I am having difficulty approaching this problem: Assume that K, Z_1, Z_2, ... are independent. Let K be geometrically distributed with parameter success = p, failure = q. P(K = k) = q^(k-1) * p , k >= 1 Let Z_1, Z_2, ... be iid exponentially distributed random variables with...

I have a random variable problem. I need to prove that my equation I came up with is a valid probability mass function. In the problem, I came up with this for my probability mass function: \Sigma 12/(k+4)(k+3)(k+2) Maple says that this does in fact converge to 1, so it's valid...

How many heads in a row would you expect to find if you toss a fair coin 8 times? I am thinking that the probability of 3 heads is 1/8 and since you have 8 tosses, that would give an E(x) of 1. So I am guessing that 3 is the number of heads one would expect to see in a fair coin...

[b]1. Homework Statement : Molecules in the combustion chamber of a rocket engine are in a high state of random motion. When the molecules leave through a nozzle in a more ordered state, will their temperature be more, less, or the same as their temperature in the chamber before being exhausted...

Hey all i struggling to understand, these concepts. would some explain to me the relationship and differences the distribution of a random variable and a probabiltiy distribution. wikipedia says this about probability distribution "The probability distribution describes the range of possible...

Homework Statement Let X and Y have JD f(x,y) = e^-y, 0<x<y Find: a) E(X|Y=y), E(Y|X=x) b) density function of R.V. E(X|Y), E(Y|X) The Attempt at a Solution a) I have found E(X|Y=y) = y/2 for y>= 0 E(Y|X=x) = x +1 for x>= 0 by finding fx(x) = ∫(x to infinity) e^-y dy = e^-x...

Could someone point me to a book that has a proof of the above statement? Thanks in advance!

I was just wondering. I have been looking all over for an answer to this question but I can't seem to find any. I read a biography about Einstein recently and it said that when quantum mechanics first came about he said (something like): "I will not deny its usefulness, only the conclusions...

Homework Statement Ok, I have 2 questions: 1. Nicotine levels in smokers can be modeled by a normal random variable with mean 315 and variance 1312. What is the probability, if 20 smokers are tested, that at most one has a nicotine level higher than 500? 2. fX,Y (x,y) = xe-x-y...

Homework Statement Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying...

For random variables Xk~N(0,1) is there any way of representing the following sum by another random variable? lim_{n\rightarrow \infty}\sum_{k=0}^n X_k thanks

If I have random variable, P ~ U(1,2), am I correct in thinking that xP ~ U(1,2) also ? (where x is some constant), or does the range change? Thanks.

Homework Statement X is exponentially distributed with mean s. Find P(Sin(X)> 1/2) Homework Equations fX(x) = se-sx, x\geq 0 0, otherwise FX(x) = 1 - e-sx, x\geq 0 0 otherwise The Attempt at a Solution Let Y = sin X FY (y) = P(Y\leq y) = P(sinX \leq Y) = P(X \leq...

Homework Statement Let X1...XN be independent and identically distributed random variables, N is a non-negative integer valued random variable. Let Z = X1 + ... + XN (assume when N=0 Z=0). 1. Find E(Z) 2. Show var(Z) = var(N)E(X1)2 + E(N)var(X1) Homework Equations E(Z) = EX (E(X|Z))...

I am a little shaky on my probability, so bear with me if this is a dumb question... Anyway, these two random variables are given: X : Poisson (\lambda) \lambda : Exponential (\theta) And I simply need the marginal distribution of X and the conditional density for \lambda given a value for X...

Hello, Suppose that a random variable Y is formed by transforming another random variable X by using the tranforming function g(.). That is: Y=\,g(X) Now, given that we have the Probabililty Density Function (PDF) of both RVs: f_Y(y)\mbox{ and }f_X(x), how can we specify g(.)? I didn't...

"If a random variable has a probability density function, then the characteristic function is its Fourier transform" - http://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)#Definition". I have never come across a random variable that did not have a probability density...

Homework Statement A text file contains 1000 characters. When the file is sent by email from one machine to another, each character (independent of other characters) has probability 0.001 of being corrupted. Use a poisson random variable to estimate the probability that the file is transferred...

please corret me if i am incorrect in my understanding of a RV,PMF or anything else but as i understand it a random variable simply maps a expirmental outcome to a real number. And a probability mass function simply gives the probabilty that a number will occur. Now my question is this: why...

Hi, I'm sure this has been tried but I was just wondering if it's possible to use the distribution of stars and planets in the sky and see how much that deviates from true randomness. With that calculation in mind, I would then think it's possible to determine the gravitational force present...

My impression from looking through the internet is, that it is a well-accepted opinion that stock market calculations are based on the random walk hypothesis. A friend of mine says otherwise. Could you provide some opinions or rather references to prove one view or the other?

This is a very random question. Why does most males prefer hot girls over cute girls (provided that they're both different type of looks)?

Hi, I'm reading Data Structures and Algorithm Analysis in Java (Second Edition) and I'm on page 178, if anyone owns the book. I know It's a computer science book and this is a math subforum, but the question is largely a mathematical one involving probability. You just need to understand what a...

What is the difference between Random Signal and Random Process? A random process does not necessarily imply and ensemble of random signals. Is this correct? M

Homework Statement T_{x} is the passage time min{n : x(n) = x} for paths starting from x(0)=0 Show: \lim_{x\rightarrow +\infty}E_{0}(e^\frac{-\alpha\\T_{x}}{x^2}) = e^\-\sqrt{2\alpha} for any \alpha ≥ 0 Homework Equations The Attempt at a Solution I came up with the...

Hallo, I'm looking for a Random function in c++. i tried to use in the function rand()% but it does not generate a truly uniformly distributed random number in the span (since my span is large. 100000*100000). in other word it dosent generate a random number in equal probabilty in lage...