Random variable Definition and 268 Threads

The random variable X assumes the values 1,2,3 and 4 with equal probability. Find the density functions of the following variates: Attempted solutions: X 1 2 3 4 Pr(X) 1/4 1/4 1/4 1/4 a) Y=1-2X Y -1 -3 -5 -7 Pr(Y) 1/4 1/4 1/4 1/4 b) Z= X/(X+1) Z...

Let X be a discrete random variable that can assume the values -1, 0,1,2,3,4 with the probabilities 1/6, 1/12, 1/6, 1/4, 1/12, 1/4. Find the probability densities of the following random variables: a) Z= X^2 + 1 h(y)= f(g^-1(y)) Attempted Solution X= -1 0 1 2 3 4 Z=...

Ok, since nobody answered my last problem, I simplify. :) Let Z = γ1X1 + γ2X2, where the gammas are just constants p(Z) = exp(Z)/(1 + exp(Z)) X1 and X2 are bivariate normal and put Y = α + β1X1 + β2X2 + ε where ε ~ N(0,σ). Now, we want to find f(p(Z)|X1,Y). In this case, is it legal...

Data is collected on the number of fish caught per day on a month long fishing expedition. It is hypothesised that the data are consistent with a negative Binomial random variable ,X , starting at 0, so that X~Neg Bin(k,p) where E[X]=k(1-p)/p and Var =k(1-p)/p^2 . However, before a hypothesis...

Hello everyone! I am stuck in my research with a probability density function problem.. I have 'Alpha' which is a random variable from 0-180. Alpha has a uniform pdf equal to 1/180. Now, 'Phi' is a function of 'Alpha' and the relation is given by, Phi = (-0.000001274370471*Alpha^4) +...

Hello everyone, I'm having a little trouble with a probability problem with three parts; I think I'm having trouble wrapping my head around just what's going on here. If anyone could give me a starting point, I'd appreciate it. Here's the problem (Billingsley 5.1) (X a random variable)...

Let X be a continuous random variable. What value of b minimizes E(|X-b|)? Giv Homework Statement Let X be a continuous random variable. What value of b minimizes E(|X-b|)? Give the derivation The Attempt at a Solution E(|X - b|) E[e - \bar{x}] = E(X) E(|E[e - \bar{x}] - b|)...

Homework Statement The problem is to find sufficient and preferably also necessary conditions on random variable X such that its characteristic function g(x) satisfies the limit property: \lim_{t\to0}\frac{1-g(\lambda t)}{1-g(t)}=\lambda^2 I may assume X is symmetric around 0, so the...

Hi all, I am having trouble with the concept of joint pdf's. For example - a set Z1,Z2,...ZN are each gaussian rv. Let Z1~N(0,1), let X be +1 or -1 each with probability 0.5. Z2=Z1X1, so Z2 is ~N(0,1). (I assume this to be As Z2 is just Z1 multiplied by a simple factor, an instance...

Homework Statement There is a parking lot outside a building with n evenly spaced parking spaces that are numbered 1 through N with parking space #1 being closest to the entrance of the building, and parking space #n being the furthest away from the entrance to the building. A driver enters...

A random variable is defined as a function from one set, called a sample space, to another, called an observation space, both of which must be underlying sets of probability spaces. But often when people talk about a random variable - as in definitions of a particular, named distribution, such...

Homework Statement I'm wondering how I go about calculating the expectation of a random variable? Is it a different process for a discrete and a continuous? Can you show me an example? Say Poisson and expoential? Also, in the formula Var(X) = E[X^2] - (E[X])^2 how does one...

Homework Statement part iv confuse me,especially the limits for y please look to my answer for this part and comment Homework Equations The Attempt at a Solution i) I got c = 1/3 ii) P(X^2 >=1)=P(X>=1) + P(X<= -1) = 7/9 iii) P(X-1>=-1/4) = P(X>= -1/4+1)=37/576 iv) we find...

What is the PDF of the exponential of a Gaussian random variable? i.e. suppose W is a random variable drawn from a Gaussian distribution, then what is the random distribution of exp(W)? Thank you!

Homework Statement Lets say I roll 2 fair dice and take the sum of the square of each dice. What formula will be the variance? Homework Equations var(x)=e(x^2)-e(x)^2The Attempt at a Solution For dice A; E(A)=3.5 E(A^2)=91/6 ^ same for dice B. VAR(A^2+B^2)=E(A^4)-E(A^2)^2+E(B^4)-E(B^2)^2 ?

Hi Experts, I'm working in industry and have an application requiring some expert knowledge on statistics/probability. I have a probability distribution function (PDF) for a Gaussian random variable. I know the standard deviation of the PDF. I also know total number of experiments conducted...

The probability density function of the time customers arrive at a terminal (in minutes after 8:00 A.M) is f(x)= (e^(-x/10))/10 for 0 < x c) Determine the probability that: two or more customers arrive before 8:40 A.M among five that arrive at the terminal. Assume arrivals are...

Hi everyone, I'm confused about Durrett's formal definition of a random variable, as well his formal notions of probability spaces in general. I always try to make abstract definitions concrete through simple examples, but I can't wrap my head around this one: Durrett defines: X is a random...

Hi all, I have a question relating to the sum of continuous random variable probabilities that I hope you can help to answer. In any probability density function (pdf), dealing with discrete or continuous random variables, the sum of the probabilities of all possible events must equal 1...

For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value from searching in internet I found that E{X|X>a}=a+E{x} but I can not prove it Help please

Homework Statement For an exponential random variable X with rate u What is E{X|X>a} where a is a scale value Homework Equations The Attempt at a Solution

Homework Statement 10 face cards are face down in a row on a table. Exactly one of them is an ace. You turn the cards over one 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...

Homework Statement Let the random variable X represent the length of the side of a square. It has a uniform distribution over the interval (0, 5). What is the cumulative distribution function for the area of the square, Y? Homework Equations F(x) = 0.2x (the cdf of the side). The...

In an analog to digital conversion and analog waveform is sampled, quantized and coded. A quantized function is a function that assigns to each sample value x a value y from a generally finite set of predetermined values. Consider the quantized defined by g(x)=[x]+1, where [x] denotes the...

Homework Statement [/b] There are two problems I need help with, which are posted below. Any help is appreciated. 1)Let X have a Poisson distribution with parameter λ. If we know that P(X = 1|X ≤ 1) = 0.8, then what is the expectation and variance of X? 2)A random variable X is a sum of...

Homework Statement Z is a random variable. P(X=a) = p1 P(X=b) = p2 P(X=c) = p3 P(X=d) = p4 Find the variance. Homework Equations Var(X) = E(X2) - E(X)2The Attempt at a Solution Okay so for the E(X2), I am currently very confused. My professor gave us this formula where E(X^2) =...

Homework Statement random variable of X has pdf: f(x) = (3/16)*x2 from interval (-2,2). Also, E(X) = 0, and E(X2) = 12/5. Find the pdf of Y = X2 Homework Equations The Attempt at a Solution I don't really know where to start.

Hi, I am interested in the product of a Gaussian random variable with itself. If X is Gaussian then what is X^2? We know that the resultant variable of the product of two independent Guassian variables is still Gaussian but I am afraid that this is not true when you multiply it with itself. Is...

X is a random variable with a continuous distribution with density f(x)=e^(-2|x|), x e R How would you calculate E(e^(ax)) for a e R? Will it be right to take a certain range of a? And also, can you take the bounds for the integral to be between -Infinity and Infinity?

Hi there, As many texts' discussion, we usually use a variable x for any value randomly picked. For a Bernoulli trials, i.e. each random variable x can either be successful or fail. If the probability of success if p and that of failure is q=1-p, then the expectation value of x would be...

Homework Statement http://s359.photobucket.com/albums/oo40/jsmith613/?action=view&current=MathQUUU.pngHomework Equations The Attempt at a Solution So I know that k = 1 But if F(>3) = 1 then why does F(3) also equal 1 Thanks

Hello, I am given a random variable X with a p.d.f. fX(x;\theta) (depending on a certain deterministic parameter \theta) and I want to consider N sampled observations of that variable: x1,...,xN. Is it correct to consider each observation as a separate random variable xi with the same pdf...

Homework Statement find the characteristic equation of a binomial variable with pmf p(x) =\frac{n!}{(n-k)!k!}*p^{k}*(1-p)^{n-k}Homework Equations characteristic equation I(t) = \sump(x)*e^{tk}The Attempt at a Solution I(t) = \sum\frac{n!}{(n-k)!k!}*(p^{k}*(1-p)^{-k}*e^{tk})*(1-p)^{n} i am...

Homework Statement From past experience, a professor knows that the test score of students taking a final examination is a random variable with mean 65. Give an upper bound on the probability that a student's test score will exceed 75. Homework Equations None that I know of. The...

Homework Statement A trial consists of tossing two dice. The result is counted as successful if the sum of the outcomes is 12. What is the probability that the number of successes in 36 such trials is greater than one? What is this probability if we approximate its value using the Poisson...

Hello, given a continuous random variable x with a known PDF, how can we determine in general the PDF of the transformed variable f(x) ? For example f(x)=x+1, of f(x)=x2 ... ? Also, if we have two random variables x,y and their PDF's, is it always impossible to determine the PDF of f(x,y)...

Homework Statement Hi, at the moment I am trying to revise for my Probability exam, and a couple of the questions on the past paper are as follows, however I can find nothing in our notes that is of any use! Any help would be greatly appreciated, thankyou. i) Two random variables X and Y...

Howdy guys. Given that X is a random variable how would you prove |X| to be one too? Thanks for any suggestions!

Homework Statement Let X and Y be jointly absolutely continuous Random Variables. Suppose X~Exponential(2) and that P(Y>5|X=x)=e-3x. Compute p(Y>5).Homework Equations X~Exponential(2) means that its a exponential distribution integrated from -inf to inf, then sub lambda as 2. The Attempt at...

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)

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...