Random variable Definition and 268 Threads

Hello all, I have the following question: Assume (\Omega, \mathcal{F},P) = ([0,1],\mathcal{B}([0,1]),\lambda), where \lambda is Lebesgue mesure, so is X(\omega) = \frac{1}{\omega} a random variable defined on this probability space? If yes, then can I say that X is bounded a.s. because the...

There are no Bayesian Networks for continuous random variables, as far as I know. And the Netica Bayesian Network software discretize continuous random variables to build bayesian models. Are there any reasons for this? Has anyone proposed continuous random variable bayesian networks?

Homework Statement Let X be a posative random variable with probability density function f(x). Define the random variable Y by Y = X^2. What is the probability density function of Y? Also, find the density function of the random variable W = V^2 if V is a number chosen at random from the...

Homework Statement X and Y two independent random variables with distribution U(0, 1/2). Find the density of (X + Y)2|X - Y > 0 The Attempt at a Solution I was hoping this would be simpler, but somehow I always end up with nothing. The only thing I can work out just fine is that P(X...

Homework Statement The RV X has parameter p>0 and distribution: fX(x) = pxe-px for x \geq 0 and is 0 otherwise (The subscript X is a capital letter, as is the X mentioned below in the e4X) If we are to consider the RV D= e4X, determine the range and distribution fD(d) Homework...

Hi All, i got a short question concerning the ev of a monotone decreasing function. when i got a nonnegative random variable t, then its ev (with a continuous density h(.)) is given by E(t)=[int](1-F(t))dt Then if v is a nonpositive random variable, is its ev given by...

suppose we have random variable defined a function of another random variable such that Y = \mathbb{E}(X) it seem then Y is a constant. then \mathbb{E}(Y) = \mathbb{E}(X) does this even make sense ?

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...

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...

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...

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...

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) =...

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...

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

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...

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...

Hi if someone can please help me to this question? PLease? Thank you maria http://img21.imageshack.us/img21/9793/statistikh4.jpg

Homework Statement position of a random point with coordinates (x; y): equal probability inside a square whose side is 1 and the center of which coincides with the origin. Determine the probability density of Z = XY Homework Equations The Attempt at a Solution

Homework Statement Suppose U follows a uniform distribution on the interval (0, 2pi). Find the density of sin(U) Homework Equations The Attempt at a Solution Well if U ~ (0, 2pi), then sin(U) should follow a distribution on [-1, 1]. I know one way to do tackle such problems is to...

Homework Statement A card is drawn at random from an ordinary deck of 52 cards and its face value is noted, and then this card is returned to the deck. This procedure is done 4 times all together. Let X be the total number of aces selected and Y = \cos(\pi X/2). E[Y] = ? Homework Equations...

Homework Statement The probability mass function of a random variable X is: P(X=k) = (r+k-1 C r-1)pr(1-p)k Give an interpretation of X. Homework Equations The Attempt at a Solution The PMF looks like the setup for a binomial random variable. The first combination looks like you...

Homework Statement Let X be a discrete random variable with probability mass function p given by: [FONT="Courier New"] a ...| -1 .| 0 ..| 1 ..| 2 -----+-----+-----+-----+--- p(a) | 1/4 | 1/8 | 1/8 | 1/2 and p(a) = 0 for all other a. a.) Let random variable Y be defined by Y = X^2...

Hi, just started learning probability & need some help in understanding... "The binomial random variable X associated with a binomial experiment consisting of n trials is defined as X = the number of S's among the n trials. Suppose, for example, that n = 3. Then there are 8 possible...

Homework Statement Homework Equations Σ(n*2/5*(3/5)^(n-1)=5/2 The Attempt at a Solution First I found the number of tosses needed to get heads, but I don't understand how to interpret this in the E[X] formula. I know that my p(x)=.40 what is my x ? "tails for the first time"...

If X is a normal rv with mean 80 and standard deviation 10, compute the following probabilities by standardizing: P(|X-80| <= 10) I know how to determine the probability without absolute value, but this confuses me. Any help?

Homework Statement Let X be a random variable with distribution function px(x) defined by: px(0) = a and px(x) = Px(-x) = ((1-a)/2)*p*(1-p)^(x-1), x = 1,2... where a and p are two constants between 0 and 1, and px(0) is meant to be the probability that X=0 a) What is the mean of X...

I am trying to explore a number of things regarding the entropy of random strings and am wondering how a character set of random size would affect the entropy of strings made from that set. Using the following formula, I need to take the log of a discrete random variable H = L\log_2 N...

Homework Statement Has anyone heard of function of function of random varibale. That is the pdf of a random variable is a function of another random variable. If yes can some give reference for the same. Homework Equations The Attempt at a Solution

The children in a small town own slingshots. In a recent contest 4% of them were such poor shots that they did not hit the target even once in 100 shots. If the number of times a randomly selected child has hit the target is approximately a Poisson random variable, determine the percentage of...

A random variable (RV) is a function that maps events in our probability space to real space. So it seems to me a random variable is a way to quantify(into real space) the physical events in our probability space? Is my understanding correct? Saurav

Homework Statement Let the join probability density function of ZX and Y be given by f(x,y)=\left\{\stackrel{2e^{-(x+2y)}\ \ \ \ \ if\ x\ \geq,\ \ \ y\ \geq\ 0}{0\ \ \ \ \ \ \ otherwise} Find E(X^{2}Y) Homework Equations I approached this problem using a theorem from the book that states...

If W=g(X) is a function of continuous random variable X, then E(W)=E[g(X)]= ∞ ∫g(x) [fX(x)] dx -∞ ============================ Even though X is continuous, g(X) might not be continuous. If W happens to be a discrete random variable, does the above still hold? Do we still integrate ∫...

Homework Statement Let X denote the lifetime of a radio, in years, manufactured by a certain company. The density function of X is given by f(x)=\left\{\stackrel{\frac{1}{15}e^\frac{-x}{15}\ \ \ \ if\ 0\ \leq\ x\ <\ \infty}{0\\\\elsewhere} What is the probability that, of eight such...

This is not homework. Case I is mostly for background. The real questions are in Case II. Case I (one dimension): a. Suppose X is a continuous r.v. with pdf fX(x), y = g(x) is one-to-one, and the inverse x = g-1(y) exists. Then the pdf of Y = g(X) is found by f_Y(y) = f_X(g^{-1}(y) |...

Hi, anyone help please. Let X and Y are independent uniform random variables over the interval [0,1] E[|X-Y|a]=? where, a>0

"Subtracting out" a random variable let X be a discrete R.V. and let Y = f(X) for some function f. I wish to find a function g, such that Y and Z = g(X) are independent, and also such that the uncertainty H(Z) is maximized. For example, suppose X is uniformly distributed over...

Hello, In a paper, the authors defined an exponential Random Variable (RV) as X_1 \mbox{~EXP}(\lambda) where \lambda is the hazard rate. What will be the distribution of this RV: f_{X_1}(x)=\lambda e^{-\lambda x} or f_{X_1}(x)=\frac{1}{\lambda} e^{-\frac{x}{\lambda}} Thanks in advance.

Continous Random Variable HELP PLEASE! Scores on a particular test are normally distributed in the population, with a mean of 100 and a standard deviation of 15. What percentage of the population have scores ... a) Between 100 and 125 b) Between 82 and 106 c) Between 110 and 132...

Homework Statement I have attached the problem statement Homework Equations Also find attached The Attempt at a Solution My attempt is attached together with the problem statement and the relevant equations.

The question is: if X is an exponential random variable with parameter \lambda = 1, compute the probability density function of the random variable Y defined by Y = \log X. I did F_Y(y) = P \{ Y \leq y \} = P \{\log X \leq y \} = P \{ X \leq e^y \} = \int_{0}^{e^y} \lambda e^{- \lambda x} dx =...

Homework Statement Suppose a random variable X has probability density function(pdf) f(x) { 1/3 for 1 \leq x \leq 4 find the density function of Y= \sqrt{X} The Attempt at a Solution y=g(x)=\sqrt{x} so g^-1(y)=x=y^2 A= \{ x: 1 \leq x \leq 4 \} is monotonic onto B= \{y: 1 \leq...

halw could anyone help me in writing this project in MATLAB ?? A random variable X is observed at certain experiment. 100,000 samples of this random variable are stored in a vector called samples. 1. Use MATLAB to read the samples of this random variable. To read these samples you...

Let X and Y be random variables. X ~ N(u,s^2) Y = r ln X, where r is a constant. What is the distribution of Y? (This is not a homework problem. It's just related to something I was curious about, and I can't figure out how to solve this, if it is solvable...)

Homework Statement 5 men and 5 women are ranked according to exam scores. Assume no two scores are the same and each 10! rankings are equally likely. Let random variable X denote the highest ranking achieved by a woman e.g. X=2 means the highest test score was achieved by 1 of the 5 men and the...

Homework Statement Problem statement is underlined. Having problems to prove this. Homework Equations F(x) = ∫ f(x) dx Question relating to cumulative distributive function. Part ii requiring to relate cumulative distributive function to probability density function. The Attempt...

Let X be a random variable representing the number of times you need to roll (including the last roll) a fair six-sided dice until you get 4 consecutive 6's. Find E(X)? answer is 1554. I get confused with this, probability { X > n-5 }. I know that the last for throws must be 6's and the one...