Density function Definition and 182 Threads

Homework Statement Let X and Y be independent and suppose that each has a Uniform (0,10) distribution. Let Z = min{X, Y }. Find the density fZ(z) for Z. Homework Equations The Attempt at a Solution i'm sorry but i really don't know how to handle this.

Hi guys, I'm working through a problem right now and would like to pick your brains on some stuff. I have an function: $$ f(r,\phi)= -\frac{1}{3} -cos(2\phi)(\frac{a^2}{r^2}) \hspace{0.5cm} for \hspace{0.5cm} a<r<b $$. I'm working in radial coordinates so r is the distance from a center and...

suppose you have two random variables X and Y which are independent, we want to form a new random variable Z=XY, if f(x) and f(y) are density functions of X and Y respectively what is the density function of Z? I tried taking logs and applying convolution, but it did not really work

Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=69371&d=1399142463 2. The attempt at a solution I am working on the last problem now. Here is what I have got so far. Basically I have converted the coordinate space wave function to a momentum space wave...

Homework Statement Problem is attached in this post Homework Equations Problem is attached in this post The Attempt at a Solution I can solve the integral since I know P(X) = ∫f(x)dx=1 from a to b, however I can't figure out how to derive the function from the given graph...

Homework Statement I need to find the probability density function given the eigenfunction Homework Equations \psi=C\exp^({\frac{ipx}{\hbar}-\frac{x^2}{2a^2}}) The Attempt at a Solution I tried to square the function but that gave me a nasty integral that I could not solve. I...

Hello, in a certain context I had to deal with a random variable Y=e^X, where X follows a standard normal distribution, i.e. X\sim N(0,1). I had to calculate the probability density function of Y, which did not seem to be difficult, and I obtained: f_Y(y)=\frac{e^{-\frac{1}{2}...

Homework Statement Let the probability density function##f(x) = (3/4) \cdot (1-x^2)## if x is between -1 and 1, and let ##f(x)=0## otherwise. What is the probability of ##P(X \leq 0.8 | X>0.5)##? Homework Equations The Attempt at a Solution I assume I have to rewrite the p.d.f. into a joint...

Given a plane with three points, (0,−1), (2,0), and (0,1) with x-axis and y-axis connecting three points to make a triangle. Suppose this triangle represents the support for a joint continuous probability density Pick one of the following: The marginal density f(y), defined as ∫f(x,y)dx...

Given a plane with three points, (0, -5), (10,0), and (0, 5) with x-axis and y-axis connecting three points to make a triangle. Suppose this triangle represents the support for a joint continuous probability density What can we say about the marginal density f_2(y)? Are they going to be...

http://gyazo.com/02812d5d8f1d07c72153c9f66740e147 I've dealt with integrals with infinity before. When considering the part x >= 1 , do I take the limit as if it's a very large number? i.e. ## \int_0^{\infty} x^{-2.5} \ dx = 2/3 ## ?

I am trying to create a simple implementation of the Bayes decision rule with minimum error criterion and I am running into a problem. Specifically, if I have a data set consisting of a number of feature vectors stored in rows, how can I generate a probability density function from this data...

If g and f are two normalized probability density functions is it then true in general that the convolution of f and g is normalized too?

1. Homework Statement +Relevant equations+Attempt at a solution Hi, I'm stuck on a problem. I have that [/itex]P(x,t|y,0)[/itex] represents the probability density that a function has the value x at time t knowing it had the value y at time [/itex]t_0=0[/itex] . Where...

Give me an example like: X: random variable representing the sum of 1 dice roll p: probability of getting a dice result E(X) = sum of X*p = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) +6(1/6) BONUS POINT: what would be the E(X) for 3 dice rolls? Sorry, I am really dumb. I am...

Homework Statement Show the gamma density function integrates to 1.Homework Equations Assume α > 0, λ > 0, t > 0 g(t) = \frac{λ^α}{\Gamma (α)} t^{α-1}e^{-λt} \Gamma (α)= \int_0^∞ t^{α-1} e^{-t} dt The Attempt at a Solution Show \int_0^∞ \frac{λ^α}{\Gamma (α)} t^{α-1}e^{-λt} dt = 1...

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...

Hello. I have problem with one task of probability theory. Hope that someone will be able to help me! The task: The rod is dividing in two parts accidentally. (Division is evenly distributed, don't know if its good saying in english). Find the density function of random variable X which is...

Hi there, So regular i thought that the procedure was F(s) = ∫s0 f(x) dx However i am doing a problem with a kinked pdf and it is telling me to do something like F(s) = ∫s0 f(s) ds for 0=<s>=1/2 then... F(s) = F(1/2) + ∫s1/2 f(s) ds I am confused at the process of using f(x) or...

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 Given f(x;λ) = cx^{2}e^{-λx} for x ≥ 0 Determine what c must be (as a function of λ) then determine the maximum likelihood estimator of λ. The Attempt at a Solution So I'm supposed to integrate this from 0 to infinity, from what i can gather. Let u = x^{2}, du...

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 "Suppose that a liquid has an appreciable compressibility. Its density therefore varies with depth and pressure. The density at the surface is ρ0 (a) Show that the density varies with pressure according to ρ=ρ0ekp where P is gauge pressure at any depth and k is the...

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.

I have a conceptual problem. Homework Statement I was given a charge distribution for an electron cloud of a hydrogen atom in the ground state - ignoring the nucleus. Homework Equations charge density: ρ=charge of electron/(pi*Bohr radius^3)*exp(-2r/Bohr radius) The Attempt at a...

Homework Statement Let f(x,y) = 24xy where x=[0,1], y=[0,1], x+y=[0,1] Find E[X] and E[Y] Homework Equations E[X] = the integral from neg. infinity to positive infinity of x * f_X(x) dx where f_X is the marginal density function of X. The Attempt at a Solution f_X is found by...

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, 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...

If I am given the CDF of a piecewise mixed distribution density starting from a and ending at b, would the expected value just be a + integral(all the pieces) ?

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...

Homework Statement This is not really a homework just studying but I'm kinda stuck. So I am trying to find out how to formally write down the Charge Density for any distribution. Although I will not get into Green's Function or how to find V, I got that fine. My example will be a Rod of...

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 X and Y be independent random variables each having the Cauchy density function f(x)=1/(∏(1+x2)), and let Z = X+Y. Show that Z also has a Cauchy density function. Homework Equations Density function for X and Y is f(x)=1/(∏(1+x2)) . Convolution integral =...

Homework Statement The probability density function of a random variable y is: f(y) = 100ye^{-10y}, if y>0 f(y) = 0 otherwise What is the probability that 45y <= 10? Homework Equations E(y) = ∫yf(y)dy Var(y) = ∫(y-E(y))f(y)dy The Attempt at a Solution I...

Homework Statement If U is uniform on [−1, 1], find the density function of U^2. Homework Equations f(u) = 1/(b-a) The Attempt at a Solution I actually solved the problem already, but I am having trouble defining what the boundaries are for U^2. My work is uploaded in paint...

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 -infinity<x<infinity x> theta f(x) = \frac{\lambda}{2}e^{-\lambda (x-\theta)} F(x) = \int_{-\infty}^x f(x) dx Homework Equations The Attempt at a Solution Homework Statement \int \frac{\lambda}{2}e^{-\lambda (x-\theta)} dx = -\frac{1}{2}e^{-\lambda(x-\theta)}...