Density function Definition and 182 Threads

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...

For the density function for random variable Y: f(y) = cy^2 for 0<= y <= 2; 0 elsewhere We are asked to find the value of c. I did a definite integral from 0 to 2 of cy^2. I get c = 3/8. Why would the book show an answer of c = 1/8? Is this an error on their part or am I missing something...

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...

Hi guys i am struggling in how to find the density function for X^2Y^2 and max(X,Y). Here's the scenario: Suppose a random variable X has the Uniform distribution on the interval [-1,1]. Suppose a random variable Y has the exponential distribution with parameter lamda=2. X and Y are...

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.

The energy density function for the electric field in vacuum is u=\dfrac{\epsilon_0}{2}E^2 And the cited textbook result for the energy density inside a dielectric is: u=\dfrac{\epsilon_0 \epsilon_r}{2}E^2 Now, one way to reach the upper formula is to look at the energy as...

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)...

Problem : A random variable X has probability density function f(n) = \begin{cases} Ax, & \mbox{0 lessthan equal x less than 5 } \\ A(10-x), & \mbox{5 less than equal x less than 10 }\\ 0, & \mbox{otherwise } \end{cases} i)Determine A ii)Find P(2.5 <= X <= 7.5) Solutions i) let P(A)...

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 Two random variables, x and y. Density functions are m(x) and f(y), respectively. x is defined on [0,1] and y on [0,1-\rho]. I also know that \int_{0}^{1} m(x) \,dx = 0.5 \int_{0}^{1-\rho} f(y) \,dy = 0.5 Knowing that f(y) is essentially a transformation of m(x)...

I have a region R = {(x,y): |x| + |y| <= 1} I have sketched the graph on the x-y plane and shaded in the region R (I got a diamond). How do I find the area of R and hence find the joint density function f(x,y) and how do I specify the region for which f(x,y) is non-zero.

Homework Statement Given the joint density, f(x,y), derive the probability density function for Z = X + Y and V = Y - X. Homework Equations f(x,y) = 2 for 0 < x < y < 1 f(x,y) = 0 otherwise. The Attempt at a Solution For Z = X + Y, I can derive the fact that, f_Z(z) =...

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...

p(t) = Ce-Ct i know P(t) is the fraction of the group surviving t years or less now the question is: suppose a patient has a 70% probability of surviving at least 2 years, find C. to find c i would take the integral of p(t) but what would my limits be? surviving 2 at least 2 years, so...

Homework Statement Let X and Y have JD f(x,y) = e^-y, 0<x<y Find: a) E(X|Y=y), E(Y|X=x) b) density function of R.V. E(X|Y), E(Y|X) The Attempt at a Solution a) I have found E(X|Y=y) = y/2 for y>= 0 E(Y|X=x) = x +1 for x>= 0 by finding fx(x) = ∫(x to infinity) e^-y dy = e^-x...

Y-U(-2\pi,2\pi) find the density function of z=tan(Y) ? i had a similar question X-U(0,1) find the density function of W=a+bx the solution is W-U(a,a+b) how to solve the first question ??

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 Let X and Y be independent uniform (0,1) random variables. a. find th ejoint density of U=X, V=X+Y. b. compute the density funciton of V. Homework Equations The Attempt at a Solution Part a. is not a problem. I don't understand how the bounds for part b...

Density Function and E(x)[solved] The density function of X is given by https://webwork.math.lsu.edu/webwork2_files/tmp/equations/48/83b2bf602cc895a007a673a9a23c3c1.png If the expectation of X is E(X)=-1, find a and b. The Attempt at a Solution I'm actually working ahead of the...

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...

Homework Statement There are two parts to question, the first asks for you to find the moment of inertia I for a thin disk of uniform density, a relatively trivial problem. My problem centers around that second part, "Repeat the case where the density increases linearly with r, starting at...

Homework Statement f(x) is a density on R+ so f(x) < 0 if x < 0. Define g_(X,Y)(x,y) = f(x+y)/(x+y). Show g is a density on R^2. Homework Equations the first part is easy (showing that g is in fact >= 0. The part I am struggling with is the double integral of the g(x,y) over the positive...

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...

A point is selected at random and uniformly from the region R = {(x,y): |x| + |y| <= 1 } Find the probability density function of the x-coordinate of the point selected at random. By definition f(x) = the integral of f(x,y) over all y values. after this I'm pretty much stuck...

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...

Hello! I'm taking a mathematics course in probability and stochastic processes and we started covering the CDF (cumulative distribution function) which i understand perfectly and then the PDF (probability density function). The PDF was defined to be the derivative of the CDF. Now, the CDF is...

Suppose that h is the probability density function of a continuous random variable. Let the joint probability density function of X, Y, and Z be f(x,y,z) = h(x)h(y)h(z) , x,y,zER Prove that P(X<Y<Z)=1/6 I don't know how to do this at all. This is suppose to be review since this is a...

Assume that two random variables (X,Y) are uniformly distributed on a circle with radius a. Then the joint probability density function is f(x,y) = \frac{1}{\pi a^2}, x^2 + y^2 <= a^2 f(x,y) = 0, otherwise Find the expected value of X. E(X) = \int^{\infty}_{- \infty}\int^{\infty}_{-...

Let X, Y, and Z have the joint probability density function f(x, y, z) = kx(y^2)z, for x>0, y<1, 0<z<2 find k \int_{0}^{2}\int_{- \infty}^{1}\int_{0}^{\infty}kxy^2z dx dy dz This integral should equal 1. Is my procedure correct so far? I don't manage to solve the integral...

I am trying to make a function which is exponential for a while, and then turns gaussian: f(l,d) = \lambda e^{-\lambda d} , 0 < d < l and f(l,d) = (1-\int_0^l \lambda e^{-\lambda d} dd) \frac{1}{\sigma \sqrt{2 \pi}} e^{-(d-l)^2/(2\sigma^2)} , l < d < \infty (That is supposed to be...

Homework Statement The probability density function is defined as f(x) = (4/81)x(9-x^2) for 0 <= x <= 3 = 0 for every other value Find the median value of the density. Homework Equations The median of a function is integral from m to infinity of f(x)dx = 1/2 The...

Could anyone help to give an example where in the same proba space, x and y have each the density function, while the joint density function does not exist? Thanks in advance, Best regards

(\Triangular" distributions.) Let X be a continuous random variable with prob- ability density function f(x). Suppose that all we know about f is that a </= X </= b, f(a) = f(b) = 0, and that there exists a value c between a and b where f is at a maxi- mum. A natural density function to...

Homework Statement A production line is producing cans of soda where the volume of soda in each can produced can be thought of as (approximately) obeying a normal distribution with mean 500ml and standard deviation 0.5ml. What percentage of the cans will have more than 499ml in them...

HI Can anybody tell me how to calculate a PDF of y, where y is a function of x, such that y = a X*X + bX + C (i.e. a quadratic equation), and X follows the Normal Distribution X ~N(0, sigma) Help anybody? Thanks