Random variable Definition and 282 Threads

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...

Homework Statement Let X represent the random choice of a real number on the interval [-1,1] which has a uniform distribution such that the probability density function isf_{X}(x)=\frac{1}{2} when -1\leqx\leq1. Let Y=X^{2} a. Find the cumulative distribution F_{Y}(y) b. the density function...

A random variable X follows a certain distribution. Now say I multiply the random variable X by a constant a. Does the new random variable aX follow the same distribution as X?

Homework Statement Compute the variance of the random variable X given by V(X) = \sqrt{E((X-E(X))^2)} where E(X) is the expectation value of random variable X Homework Equations Hint: Use parameter differentiation The Attempt at a Solution I have no idea what to do here. I've never taken...

I have two random variables X and Y, and I need to calculate E(XY). The expectation of X, E(X) = aZ, and the expectation of Y, E(Y) = bZ, where a and b are known constants and Z is a random variable. So the question is how would I calculate E(XY)? I was thinking that I could do the...

I've been asked to model a resistance as a random variable. I am not exactly sure what that entails, but I was hoping someone might give me a little bit of insight. I have one resistance that is oscillating sinusoidally, and that produces a U shaped probability distribution. As is shown in...

How do I do this p(x<1) this sign has a _ under the < n=6 p=0.1 Suppose x is a discrete, binomial random variable. Calculate P(x > 2), given trails n = 8, success probability p = 0.3 [Hint: P(x > value) = 1 – P(x <= value) <= is a < with a _ under it (tell me the number...

hi there. currently looking at the two conditions that must be met for a process to be wide sense stationary. The first constion is: E[X(t)] = constant what exactly does this mean??isn't is obvious that any random variable (with fixed time) will always yield a constant expextation. I...

Here's the qn random variable X follows uniform distribution [-a,a] and random variable Y is defined as Y=e^x find E(Y) i figure that E(Y)=E(e^x) but somehow can't carry on from there can anyone help?

I'm trying to write a program in excel to generate random variables with mean mu and standard deviation sigma. I can simply refer to the worksheet function for it but it takes forever when I have it inside a loop doing a monte carlo simulation. There is one function in excel that returns a...

I have a question, we know that a random variable X is a function that maps a real number to an event in the Sample Space. But, if X is a random variable, then the absolute value of X, say |X| is a random variable too? Why? I am almost sure that it is not because we can not tell wheter an...

So the problem gives a binomial random variable X with parameters n=5 and p=0.25 and ask for the probability P(X=1.5). The binomial probability mass function is defined only for integers. Should i approximate using the normal distribution or the poisson?

Hi.. i am doing this question for Probability Theory, to find E[x] of a continuous random variable E[x] = the integral from (0 to infinity) of 2x^2 * e^(-x^2) dx So I used integration by parts... u = x^2 du = 2xdx dv = e^(-x^2) <--- ahh... how do you integrate that. (it dosn't look like...

If you have a geometric random variable with probability mass function: P(X=n) = p(1-p)^n n = 0,1,2,3... Find the Mean and the Variance. ---------------------------- Okay, I've looked everywhere and tried everything, however, i just cannot get it. i think that your supposed...

Hello... hmm.. i am working on a homework problem, and I am kina stuck. the question reads: Suppose that X is a random variable which can take on any non-negative integer (including 0). Write P(X greater than and equal to i) in terms of the probability mass function of X and hence show...

Hi,I'm new to the site. I come with a question I was hoping soemone out there can help me set up. "The manager of a bakery knows that the number of chocalate cakes he can sell on any given day is a random variable with the probability mass function: p(x)=1/6 For x=0,1,2,3,4,5...

hello all I have been workin on some problems involving conditional probability and continuous random variables and the thing is i don't know if i get the limits correct, anyway here is the problem, check it out, any suggestions would be helpful f(y_1,y_2)...

THe Laplace random variable has a PDF that is a double exponential, fT(t)=ae^(-|t|/2) for all values of t and a, a constant to be determined. A) Find a (Answer 1/4) B)Find the expected value of T, given T is greater than or equal to -1. (Answer 1.31)

:confused: Hello I have a simple question : Let $X_n$ a random variable of same law If $V(X_n)\longrightarrow 0$ when $n\longrightarrow +\infty$ How schow that : $E(X_n)\longrightarrow C$ and $E(X_{n}^{2}\longrightarrow C^2$ and C is a constant? Thanks

I'm having trouble showing the following relation: E(exp(z)) = exp(E(z^2)/2) where z is a zero-mean gaussian variable and E() is the avg anyone can help?