# density

1. ### Posterior Distribution from Beta Density with Exponential Prior

Let $X_1,...,X_n$ be iid random variables with a common density function given by: $f(x|\theta)=\theta x^{\theta-1}$ for $x\in[0,1]$ and $\theta>0$. Put a prior distribution on $\theta$ which is $EXP(2)$, where $2$ is the mean of the exponential distribution. Obtain the posterior...
2. ### Joint probability density question2:

A drinks machine has a random amount Y (in gallons) in supply at the beginning of a given day and dispenses a random amount X during the day. It is not resupplied during the day and so X â‰¤ Y . The joint pdf is f(X,Y)=0.5 0<x<y and 0<y<2 I need to find the probability that less than...
3. ### Joint probability density question:

The joint random variables have a density $f(x,y)=x+y$ for 0<x<1 and 0<y<1 and 0 otherwise, Evaluate E(X) and E(XY) My answer for E(x)=7/12 however i feel like i may have made a mistake somewhere.
4. ### Can Probability density functions take negative values?

My question is: evaluate the pdf at fx(3) where fx(x)=(-2)/((1+x)^3) and compute value -1/32, can pdf's be negative or have i made a mistake in the previous question? Thanks!
5. ### Triple integral density of a strange shape.

x = 0 y = 0 z = 0 x + y = 1 z = x + 2y Density(x, y, z) = 3 + 2x + 2y - 2z Answer: 1/6 My Solution (not correct) \int_{0}^{1} \int_{0}^{1-x} \int_{0}^{x+2y} (3+2x+2y-2z) ~dz~dy~dx = 5/3 What did I do wrong?
6. ### Help interpreting a probability density function

Hello, I am struggling with the following question -does anyone have any ideas on how to approach it? Y has the probability density function defined by: f(y) = kÎ¸^k / y^k+1, y >= Î¸ and f(y) = 0 for y< Î¸, where Î¸>0 and k>2 Question: Why is k restricted to being greater than 2 in the...
7. ### Find the support of the density function of the random variable $X + Y$ .

The support of a function $f(x)$ is defined to be the set $\{x : f(x) > 0\}$ . Suppose that $X$ and $Y$ are two continuous random variables with density functions $f_X(x)$ and $f_Y (y)$, respectively, and suppose that the supports of these density functions are the intervals $[a, b]$ and...
8. ### Calculating a density of a sphere

An object occupies the region inside the unit sphere at the origin, and has density equal to the distance from the x-axis. Find the mass. This is my solution \int_{0}^{2 \pi} \int_{0}^{\pi} \int_{0}^{1} \sqrt{1-\rho^2 sin(\phi)^2 cos(\theta)^2} \rho^2 sin(\phi) d \rho d \phi d...
9. ### Let X be a random variable with range [âˆ’1,1] and let fX(x) be the density function of

Let X be a random variable with range [âˆ’1,1] and let fX(x) be the density function of X. Find Âµ(X) and Ïƒ^2(X) if, for |x| < 1 (a) fX(x) = |x|
10. ### Calculating density with strange shape...

Calculate the mass of solid V bounded by given planes and having density p(x,y,z) = 3 + 2x + 2y - 2z x = 0, y = 0, z = 0, x + y = 1, z = x + 2y Answer: 1/6
11. ### How to find the cdf and density?

Choose a number U from the interval [0, 1] with uniform distribution. Find the cumulative distribution and density for the random variables (a) Y = |U âˆ’ 1/2|. (b) Y = 1/(U âˆ’ 1/2)^2 .
12. ### Finding a probability density function from a distribution function and using it.

F(x,y)=1-e^[-x]-e^[-y]+e^[-x-y] So f(x,y)= e^[-x-y] if I did both partials over. I'm told to find P(X+Y>3) I can't quite get the bounds right. It's a double integral of f(x,y). Are the founds (3-y) to (infinite) for dx And 0 to (infinite) for dy?
13. ### Density and volume calculations

Hi all, I'm new to the site and far from a mathematician. I am a Coal Prep Plant Manager having trouble trying to solve a problem with a few different variables which I'll explain below. I have a sump with a total volume of 14900 litres containing a mixture of water (density of 1) and...
14. ### Probability Density Function Question

The goal of this exercise is to estimate the PDF of the following data. Any appropriate distribution(s) may be used. Any idea as to how I should do it, and what a good answer is? The data series is attached. #N/A ************** -** ********* 4.38 ********* 3.89 ********* 5.21 *********...
15. ### How to calculate P(X>=3Y) having density function

f(x,y) = 1 if 0<= x <= 2 ; 0<=y<=1 ; 2y<=x 0 (another combination) How can I calculate P(X>=3Y) ? Thanks

There are two cylinders Cylinder A and Cylinder B. There is also a hollow hole that has the same radius as cylinder A. Cylinder A weighs 100kg. Cylinder B is lighter and smaller than cylinder A. Both cylinders have the same thickness. When the edge of Cylinder B is just past the...
17. ### Probability Density Function

I have this problem: The following density function describes a random variable X. f(x)=x/25 if 0<x<5 and f(x)=(10âˆ’x)/25 if 5<x<10. find the probabilities below: A. Find the probability that X lies between 2 and 3. I'm not sure which function I'm supposed to be using.
18. ### density function

I'm getting a bit confused about basic probability notation. lets say I have y = x^2, where y and x are both random variables. Can I write the following: P(Y <= y) (c.d.f of y) P(Y <= u^2) P(Y^0.5 <= u), which equates to the c.d.f of X at X=(Y^0.5) I'm getting slightly confused...
19. ### probability density equal to a*(sin(bx))^2

Hi all, can you give me an example of dynamical system (or any chaotic system or any mathematical model ) that the probability density equal to a*(sin(bx))^2 ? Thank you .
20. ### Conditional Density

Let X be exponential with mean 1/Î»; that is, f_X (x) = Î»e^{-Î»x} , 0 < x < âˆž Find E[X|X > 1]. The way I started this was f_{X|X>1}(X)=\frac{f(x)}{\int_1^{\infty}\lambda e^{-\lambda x}dx} The solution in the book starts with f_{X|X>1}(X) = \frac{f(x)}{P\{X>1\}} Is this...