Random variable Definition and 282 Threads

Homework Statement Let X~Bernoulli(θ) and Y~Geometric(θ), with X and Y independent. Let Z=X+Y. What is the probability function of Z? Homework Equations The Attempt at a Solution I am getting PX(1) = θ PX(0) = 1-θ PX(x) = 0 otherwise pY(y) = θ(1-θ)^y for y >= 0...

Homework Statement Generate Geometric RV with Porbabilty of succcess 0.1 using only rand() Homework Equations rand() geometric rv P=(1-p)^(k-1) * p where p=0.1, k is number of trial in which we get 1st success The Attempt at a Solution rand(n)

Homework Statement Generate 1,00,000 triplets(sets of three) of Uniform random variables on [0,1]. Y be max of each triple and Z be min of each triple. Derive the densities for these RV from theory and compare histograms of Y and Z with densities found in theory. Homework Equations...

What is the Matlab code for generating 100,000 Raleigh Random Variable with sigma^2=2 using rand command only. Generate histogram and normalize it by dividing 1,00,000 times the bin width

The transformation of a random variable is well documented and there are numerous examples on the web. Most examples present univariate variable transformation utilising inverse of the transformation function. The method works whenever the transformation function is one-to-one. Let's say...

Homework Statement Continuous random variable X has probability density function defined as f(x)= 1/4 , -1<x<3 =0 , otherwise Continuous random variable Y is defined by Y=X^2 Find G(y), the cummulative distribution function of Y Homework Equations The Attempt at a...

Ok I am not sure if I should put this question in the homework category of here but it’s a problem from schaums outline and I know the solution to it but I don’t understand the solution 100% so maybe someone can explain this to me. Let X and Y be defined by: \begin{array}{l} X = \cos \theta...

1 Calculate the expected value of variable x (or E(x)) (number of trials * probability of success) 2 Calculate the variance (expected value * probability of a failure) Take everything to the right of the decimal in the variance off. Then the range of future values is E(x) plus/minus the variance.

Homework Statement A random variable X takes values 1,2,...,n with equal probabilities. Determine the expectation, R for X and show that the variance, Q^2 is given by 12Q^2=n^2-1. Hence, find P(|X-R|>Q) in the case n=100 Homework Equations The Attempt at a Solution I can show...

Given two random variables x and y, and a constant c What conditions are needed to make: Prob( w x + y < c ) \approx Prob( w x < c ), \text{ for } w \rightarrow \infty Can anyone help? I think E(x) < \infty and E(y) < \infty might do. Is this right? tks!

Homework Statement Hello, have a stats question I am hoping you guys can help with. The expectation of a function g of a random variable X is: E[g(X)] = \int^{\infty}_{-\infty} g(x)fx(x)dx where fx is the pdf of X. For example, the particular expectation I am considering right now...

This is a problem from my A levels Stats2 book. I understood the problem but one of my answers doesn't seem to be correct according to the book so I thought I better be sure! Homework Statement A piece of laminated plywood consists of 3 pieces of wood of type A and 2 pieces of type B. The...

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 There is a pin of length 4 which appear on a photograph, and the length of the image observed is y, an observation on the random variable Y. The pin is at an angle x, 0\leqx\leq\pi/2, to the normal to the film, this is an observation on the r.v. X. 1. If all angles X...

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: 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. Calculate the...

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...