Probability density function Definition and 128 Threads

A joint pdf is given as pxy(x,y)=(1/4)^2 exp[-1/2 (|x| + |y|)] for x and y between minus and plus infinity. Find the joint pdf W=XY and Z=Y/X. f(w,z)=∫∫f(x,y)=∫∫(1/4)^2*e^(-(|x|+|y|)/2)dxdy -∞<x,y<∞ Someone told me I can not use Jacobian because of the absolute value. Is that true? So...

A joint pdf is given as pxy(x,y)=(1/4)^2 exp[-1/2 (|x| + |y|)] for x and y between minus and plus infinity. Find the joint pdf W=XY and Z=Y/X. f(w,z)=∫∫f(x,y)=∫∫(1/4)^2*e^(-(|x|+|y|)/2)dxdy -∞<x,y<∞ Someone told me I can not use Jacobian because of the absolute value. Is that true? So far this...

I'm practicing the past year papers to prepare for my coming finals. Please make necessary corrections if you feel something wrong with it, thanks! Also, I'm supposed to do this in less than half an hour, so any suggestions on how to shorten this answer is really much appreciated! Homework...

Homework Statement The PDF (probability density function) of a Gaussian variable x is given by. $$p_x(x)=\frac{1}{C \sqrt{2 \pi}} e^{\frac{-(x-4)^2}{18}}$$ a) Find C b)find the probability of x≥2 --> ##P(x≥2)## Homework Equations $$ \frac{dF_X(x)}{dx} x=P(x<X≤x+Δx)$$ The...

Homework Statement A random variable x has a probability density function given by fX(x) = e-x , x ≥ 0 and an independent random variable Y has a probability density function of fY(y) = ey , y ≤ 0 using the characterisic functions, find the probability density function of Z = X + Y...

So I understand how for a continuous random variable the probability of an exact value of X is zero, but then what is the value of f(x) if it's not a probability? I thought it was a probability similar to how the pmf for a discrete random variable was a piece-wise function that gave the...

Homework Statement See figure attached. Homework Equations The Attempt at a Solution I'm having trouble getting start with this one, but here's what I've got so far. I assumed R is the signal received by the TDS. P(R=X) = \mu \quad , \quad P(R=N) = 1 - \mu Now in part...

Homework Statement The joint probability density function of X and Y is given by f(x, y) = c( x3 + xy/4 )  0 < x < 1 0 < y < 2 (a) For what value of c is this a joint density function? (b) Using this value of c, compute the density function of Y . (c) Using this value of c, nd PfX...

Homework Statement Find k such that the function f(x)=ke^{-\frac{x-\mu}{\theta}} is a probability density function (pdf), for x > \mu, \mu and \theta are constant. Homework Equations The property of a pdf says that the integral of f(x) from -\infty to \infty equals 1, that is...

If probability distribution function is flat like a rectangular signal then probability density function which is differentiation of probability distribution function will have positive and negative impulses, but probability density function cannot be negative. . what's wrong in this . . ...

Homework Statement The mean of a function is as follows: $${1 \over {a - b}}\int_b^a {f(x)\,dx} $$ So why is the mean of the PDF as follows: $$\int_{ - \infty }^\infty {xf(x)\,dx} $$ I thought it would have been this way: $$\lim \,b \to - \infty \,{1 \over { - b}}\int_b^0...

Homework Statement How can I derive the probability density function by using the Central Limit theorem? For an example, let's say that we have a random variable Xi corresponding to the base at the ith position; to make even simpler, let's say all probabilities are equal. If we have four...

Homework Statement I want to calculate the probability of a random sample falling between 2 z scores using the way real mathematicians do it not the fake way by resorting to tables. Ok, so the book outlines the equation below but says that it requires calculus which is beyond the scope of...

What is the probability density equation as a function of angle for a simple pendulum using the small angle approximation? I got 1/(2 pi θmax) sec(sqrt(g/L)t) but it doesn't seem right.

A continuous random variable X has pdf: f_X(x)=\left \{ k(x+3), 0\leq x\leq 1\right \} 0 otherwise. Find k. I solved the integral (from 0..1) and solved for the result equal to 1. Hence I got k=2/7. Is this the right way to proceed as the question continues and I want to check if I'm...

Hi there, This is my first post... and be kind on my english please...:) So here is a problem i cannot solve...I can't reach to something satifactory your ideas would be very helpful Homework Statement The probability density function f×(x) of the random variable X is zero when x<α...

Homework Statement A process is defined as: X(t) = Asin(ωt+\phi]) where A and \phiare random variables and ω is deterministic. A is a positive random variable. Determine the joint probability density function, PDF, of X(t) and X'(t) in terms of the joint PDF of A and\phi...

Hi, I have a probability density function defined by 1 / D x E . eABC/2 D is a single number E is a determinant of a matrix . is the dot product between the two sides of the function e I am pretty sure is meant to be eulers constant A is a 5x1 vector B is a 5 x 5 matrix C is a...

Hi, I have a probability density function defined by 1 / D x E . eABC/2 D is a single number E is a determinant of a matrix . is the dot product between the two sides of the function e I am pretty sure is meant to be eulers constant A is a 5x1 vector B is a 5 x 5 matrix C is...

Homework Statement A process X(t) is defined as X(t) = Asin(ωt + \phi) where A and \phi are random variables while ω is a deterministic parameter. Note that A is a positive random variable. Determine the joint probability density function, PDF, of X(t) and X'(t) in terms of the joint PDF of...

The phones offered by a cell phone company have some chance of failure after they are activated. Suppose that the density function p(t) describing the time t in years that one of their phones will fail is p(t) = 1-e^{-λt} for t ≥ 0, and 0 otherwise. The cell phone company offers its clients a...

This might not be in the right place but here it goes: Homework Statement A given periodic function in time is given u(t). I must compute the probability density function that describes u. u(t) = A sin (2π / T t + ψ) A and ψ are constants. T is the period. t is time. Homework EquationsThe...

Homework Statement Suppose X selects an integer from the set S = {0,1,...,9} and Y selects an integer from {0,...,x^2}. Find: (a) f(x,y) [joint prob density func] (b) fY(y) [marginal for Y] (c) Probability (Y <= 10 | X = 5) (d) Probability (Y <= 10 | X <= 5)Homework Equations The Attempt at a...

Homework Statement F(x)=k(1-1/x2), 1\leqx<2 Homework Equations The Attempt at a Solution How do I get the probability density function here? Simply take the derivative of this function ? 1\int2 = k(1-1/x2) Supposed to be 1 at the bottom and two at the top.

Homework Statement Let f(x,y)=xe^{-xy} x \geq 0, y \geq 1 is this a probability density function? If not, find a constant that makes it a pdf. Homework Equations To be a pdf, we must have \int_1^\infty \int_0^\infty \! xe^{-xy} \, \mathrm{d} x \mathrm{d} y=1 The Attempt at a...

Homework Statement Random voltage is defined with its probability density function: p_{\xi}(v)=2,25u(v+2)e^{-3(v+2)}+k\delta (v-2) u-Heaviside step function a) Find constant k. b) What is the probability of a random variable to take value of 2. c) Find the cumulative distribution function...

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) +...

My goal here is to at least approximately calculate the probability density function (PDF) given the moment generating function (MGF), M_X(t). I have managed to calculate the exact form of the MGF as an infinite series in t. In principle, if I replace t with it and perform an inverse...

Hello! I have been having problems with understanding how the probability density function is calculated. However, at the same time, I need it urgently for my research. Well, you could start by giving me a definition of 1. Refernce measure 2. That 'E' sign(looks like an epsilon, and I sound...

hey guys, i am really confused on something.here is the thing: i have; i=x+(x^2-y)^(1/2) and here x is uniform distribution on (a,b) y is uniform distribution on (c,d) x and y independent i need to find the probability density function of i but how? actually i don't know how to...

Homework Statement Is the PDF of something between two different bases or wavefunctions always 0? For instance, if you have the lowering operator \hat{}a - <n|\hat{}a|n> that changes to <n|\sqrt{}n|n-1> =0 I'm not sure I understand the physical scenario if this is true however.

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 X and Y are random variables with the joint density: fXY(x,y) = k*e^(-lambda * x) if 0 < y < x < infinity = 0, otherwise Find P(X + 2*Y <= 3) Homework Equations I found k = lambda^2 The Attempt at a Solution I'm not sure exactly how to solve this, but...

normally distributed random variable with mean m and variance σ2. Find the PDF of Y

Continuous random variable X is defined in the interval 0 to 4, with P(X>x)= 1- ax , 0<=x<=3 = b - 1/2 x , 3<x<=4 with a and b as constants. Find a and b. So the area under the pdf is 1, then i integrated both functions and set up my first equation. Next, it seems that the...

Homework Statement A point Q is chosen at random inside the unit square. What is the density function of the sum of the coordinates of point Q? What is the density function of the product of the coordinates of the point Q? Use geometry to find these densities. Homework Equations P(a <...

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 Roll a fair die three times Let X be the number of different faces shown all together ( X = 1,2,3 ) Find px(k) Homework Equations The Attempt at a Solution Alright so I kno that i need to get the individual probabilities of each outcome The first one where...

Homework Statement Let f(x) = (1 + ux)/2 for -1<= x <= 1 and 0 otherwise . where -1<= u <= 1 a) show f is a density Homework Equations TO show 1. f(x) >= 0 2. intergeral f (from -infinity to infinity) = 1 The Attempt at a Solution I have done 2. and proved that it is 1...

Hi everyone, I have a simple question (assuming since it was only worth 5% of total marks in the exam) about the PDF of a random variable. Given that PDF of random signal equals p(X) = \Lambda(X), where \Lambda is the triangle function, what would be the PDF of the random signal Y, Y = -3X...

Could anyone help me figure out the the probability density function (pdf) of |X|^(1/2)+|Y|^(1/2)+|Z|^(1/2) if X, Y and Z are distributed normally with mean 0 and variance 1, N(0,1) ? Thanks in advance.

Homework Statement Probability of a car starting up is 0.9 Probability of a car NOT starting up is 0.1 Cars are tested until 2 functional cars are found. Find Bernoulli probability function associated and PROVE that it is a pdf (probability density function). Homework Equations...

I'm just curious as to how to prove that a Bernoulli distribution probability function is valid (ie. that it is indeed a probability distribution function). I have a hunch that all we do is add up all of the probabilities associated to every x value, but I'm not sure. Can someone confirm this...

Probability density function after filtering Hello, I am trying to find how a random variable will transform once gone through a filter. For example, I have a random sequence x(t), going through a filter h(t). Thus, y(t) = x(t)*h(t) ; % '*' is convolution. Now I want to find out how...

I am tyring to solve the follwing problem... http://www.imagedump.com/index.cgi?pick=get&tp=549226 What is the appropriate K valuefor this to be a legitimate probability density function? Im not exactly sure of the approach to this problem...

Homework Statement Consider the wave packet defined by psi(x) = integral(limits of +infinity and - infinity) dke^(-alpha(k-k_0)^2) e^(ikx) a)What is the mean value of the momentum p barred (it's just a line over the p) of the particle in the quantum state given by this wave function...

Homework Statement Suppose that a point (X_1 , X_2 , X_3) is chosen at random, that is, in accordance with the uniform probability function over the following set S: S = {(x_1, x_2, x_3) : 0 \leq x_i \leq 1 for i =1,2,3} Determine P[(X_1 - 1/2)^2 + (X_2 - 1/2)^2 + (X_3 - 1/2)^2) \leq...

Homework Statement Let X be a random number from (0,1). Find the probability density function of Y = 1/X. Homework Equations The Attempt at a Solution I keep thinking this is easier than I am making it out to be, but the only places I find anything similar searching is on two...

How to find the probability density function of a simple harmonic oscillator? I know that for one normal node is should be a parabola but what is the formula and how do we derive it?

Please help me with this. Any suggestions are greatly appreciated. Imagine that I have a bank account. X is the amount of cash on the account at time t+1. Y is the amount of cash at time t. The amount of cash depends on the deposits made and on the amount of cash during the previous period...