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...
(\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)
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)...
[b]1. Homework Statement
A vendor at a market buys mushrooms from a wholesaler for $3 a pound, and sells them for $4 a pound. The daily demand (in pounds) from custumers for the vendor;s mushrooms is a random variable X with pdf
f(x) = 1/40 if 0 (greater than) x (less than) 40 and 0...
if x is a continuous random variable from -1 to 1...how do you find c:
f(x) = c + x , -1 < x < 0
c - x, 0 < x < 1
Do I integrate each one? Where do I go from there? Thanks!
Homework Statement
This is my 1st post here, so I will do my best. The following question is part of a number of probability density functions that I have to prove. Once I have the hang of this I should be good for the rest, here is the question:
Prove that the following functions are...
Probability Density Function...Help
The probabiltiy density function of the time to failure of an electric component in hours is f(x)=e^{(-x/3000)/3000} for x > 0 and f(x) = 0 for x \leq 0 determine the probability that
a) A component last more than 1000 hours before failure
I know how...
Not really a homework question, but a problem I don't get nonetheless.
The density of fragments lying x kilometers from the center of a volcanic eruption is given by:
D(r) = 1/[sqrt(x) +2] fragments per square kilometer. To 3 decimal places, how many fragments will be found within 10...
How do I calculate the PDF of someone's earning followed by their mean and variance?
This is the question:
Given density function
f(x) = 2.5 if 0.1 < x < 0.5
0 otherwise
The person is paid by the # of jobs they finish rather than by the hour. They get 10$/job. Calculate...
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 :)
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 \...