Density function Definition and 193 Threads

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

I feel embarassed for asking, but is there a fast way to calculate this without using integration by parts? \int 2e^(-2x)x^-1dx, 0 <= x < infinity There's supposed to be some kind of trick, right?

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 =...

Let the random variable X have the probability density function f(x). Suppose f(x) is continuous over its domain and Var[X] is bounded away from zero: 0 < c < Var[X]. Claim: f(x) is bounded over its domain. Is this claim true? I don't think a counterexample like X ~ ChiSq_1 applies...

given that x has an exponential density function ie p(x) = exp (-x) and x(n) & x(m) are statistically independent. Now y(n) = x(n-1)+x(n) what is the pdf (probability density function) of y(n)

Hey, I know how to find the expected value from the density function when it is in the form: (example) | y^2 -1<y<1 | fy =| | 0 elsewhere Ey = integral(upper limit 1, lower limit -1)[y*y^2 dy) but, what if the density function looks like this...

Hey, I know how to find the expected value from the density function when it is in the form: | fy =

Homework Statement The density function for the number of times the riders scream on a roller coaster is given by ... f(x) = \frac{1}{3\pi}(1 - cos(2x)) if 0 \leq x \leq 3\pi and 0 otherwise. Find the mean number of screams over the course of the ride. The answer: 4.71238898038...

Hi, I need a verification for this question. Can some one help me? Question: A man enters the pendulum clock shop with large number of clocks and takes a photograph. He finds that most of the pendulums were at the turning points and only a few were captured crossing the mid point. Why is it...

Homework Statement A dial indicator has a needle that is equally likely to come to rest at an angle between 0 and Pi. Consider the y-coordinate of the needle point (projection on the vertical axis). What is the probability density function (PDF) p(y)? Homework Equations I know the...

Find a constant c such that f(x,y)=cx2 + e-y, -1<x<1, y>0, is a proper probability density function. My idea: f(y) 1 =∫ f(x,y) dx -1 So I have found f(y), now I set the following integral equal to 1 in order to solve for c: ∞ ∫ f(y) dy = 1 0 Integrating, I get something like...

ok iv have been stuck on this problem for like 30 mins it says "suppose x is a continuous random variable taking values between 0 and 2 and having the probability density function below." the graph below shows a triangle with the coordinates (0,1) (2,0) then it ask what is the Probably...

Q: Given f(x) = cx + (c^2)(x^2), 0<x<1. What is c such that the above is a proper probability density function? Solution: 1 ∫ f(x) dx = 1 0 => 2(c^2) + 3c - 6 =0 => c= (-3 + sqrt57) / 4 or c= (-3 - sqrt57) / 4 => Answer: c= (-3 + sqrt57) / 4 (the second one rejected)...

Homework Statement If atmosphere can be treated as an isothermal ideal gas of constant mean molecular mass m, show that density drops exponentially with height - ρ= [ρ0]e^-z/h - where h is a constant Homework Equations ρ= [ρ0]exp^-z/h (derivation of ...) ρ=density ρ0=initial density at...

[b]1. Homework Statement A vendor at a market buys mushrooms from a wholesaler for $3 a pound, and sells them for $4 a pound. The daily demand (in pounds) from custumers for the vendor;s mushrooms is a random variable X with pdf f(x) = 1/40 if 0 (greater than) x (less than) 40 and 0...

hi.. Homework Statement what's the density function for X-Y if X and Y are independent and continously distributed on [0,1]?

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if x is a continuous random variable from -1 to 1...how do you find c: f(x) = c + x , -1 < x < 0 c - x, 0 < x < 1 Do I integrate each one? Where do I go from there? Thanks!

A continuous random variable X has the density function f(x)=x for 0<x<1 2-x for 1 _<x<2 0 elsewhere. a. Show that P(0<X<2)=1 B. Find P(X<1.2). Please see the attached file. Thank

Homework Statement Given a two-level atom with transition frequency { \omega }_{ ji } \equiv { \omega }_{a} and spontaneous decay rate \gamma, we are asked to find an expression for the "power spectral density function" S(\omega), in terms of \omega, {\omega}_{a}, and \gamma. 2. The...

Homework Statement This is my 1st post here, so I will do my best. The following question is part of a number of probability density functions that I have to prove. Once I have the hang of this I should be good for the rest, here is the question: Prove that the following functions are...

X1, X2, X3 are independent gaussian random variables. Y1 = X1+X2+X3 Y2 = X1-X2 Y3 = X2-X3 are given. What is the joint pdf of Y1,Y2 and Y3 ?

Probability Density Function...Help The probabiltiy density function of the time to failure of an electric component in hours is f(x)=e^{(-x/3000)/3000} for x > 0 and f(x) = 0 for x \leq 0 determine the probability that a) A component last more than 1000 hours before failure I know how...

Not really a homework question, but a problem I don't get nonetheless. The density of fragments lying x kilometers from the center of a volcanic eruption is given by: D(r) = 1/[sqrt(x) +2] fragments per square kilometer. To 3 decimal places, how many fragments will be found within 10...

Hi, I am having trouble with the following question. Can someone help me out? a) Find the volume of the solid that lies above the cone \phi = \frac{\pi }{3} and below the sphere \rho = 4\cos \phi . b) Find the centroid of the solid in part (a). For the volume I got 10pi which I am...

I have a question regarding the two-particle density function, in particular its Fourier transform. I know that in a liquid or gas the function n_2(\mathbf{R}_1, \mathbf{R}_2) is the probability that two particles will be found at \mathbf{R}_1 and \mathbf{R}_2. But what is the significance of...

I want a rigorous description of the density function (in cartesian coordinates) \rho(x,y,z). I suggest that we define a function M(x,y,z,V'), where V' is a volume of any given shape centered on the point (x,y,z), giving the mass contained in that volume. Then define the density function as...

How do I calculate the PDF of someone's earning followed by their mean and variance? This is the question: Given density function f(x) = 2.5 if 0.1 < x < 0.5 0 otherwise The person is paid by the # of jobs they finish rather than by the hour. They get 10$/job. Calculate...

conditional density function - need help please! given a signal x, is a random variable which is expontential with a mean of 3. it is transmitted through an additive gaussian noise channel, where the gaussian noise has a mean of -2 and a variance of 3. the signal and noise are...

Probability Density Function -- Need Help! Hi, Can someone please check my work if i did the problem correctly? thanks in advance. Here is the problem: Find the PDF of W = X + Y when X and Y have the joint PDF fx,y (x,y) = 2 for 0<=x<=y<=1, and 0 otherwise. here is my solution...

I have a problem where there are two resistors in parallel and I need to find the equivalent resistance. R1 = X and R2 = Y, and X and Y are independent random variables, uniform over the range of 100-120. If R equivalent = Z = XY/X+Y, what is probability density function of Z?

I have a problem where there are two resistors in parallel and I need to find the equivalent resistance. R1 = X and R2 = Y, and X and Y are independent random variables, uniform over the range of 100-120. If R equivalent = Z = XY/X+Y, what is probability density function of Z?

Hi Guys, I am having some trouble trying to solve a probability density function question. ...If the density function is: f(x) = 9x^3, 0 < x 1. What is the conditional probability of P(X > 0.2 | X <0.6) ?? Any help would be greatly appreciated :)

I have a problem with an integration, namely: Int(from 0 to x) (1-F(x-t)) dF(x) and do not know how to calculate...:-(

Have known a wave function, how get does distributing density function of the probability?

Suppose that X and Y are independent random variables, where X is normally distributed with mean 45 and standard deviation 0.5 and Y is normally distributed with mean 20 and standard deviation 0.1. (a) Find \ P(40 \leq X \leq 50, \ 20 \leq Y \leq 25). Ans. ~0.5 (b) Find \...