Density function Definition and 182 Threads

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...

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]?

... ...deleted

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 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...

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 \...