Hello,
i m trying to evaluate the following:
r*x - r*y ≤ g, where r,x,y are nonnegative random variables of different distribution families and g is a constant nonnegative value.
Then, Pr[r*x - r*y ≤ g] = Pr[r*x ≤ g + r*y] = ∫ Fr x(g + r*y)*fr*y(y) dy, where F(.) and f(.) denote CDF and...
If the distribution of a sum of N iid random variables tends to the normal distribution as n tends to infinity, shouldn't the MGF of all random variables raised to the Nth power tend to the MGF of the normal distribution?
I tried to do this with the sum of bernouli variables and...
Hi,
http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf (see page 8, sum of two independent random variables).
I don't understand why they had to go further into the limits, 1 < z < 2. Why do they have to do that? And also, where did they get it...
I don't completely understand why the area of the proof circled in red is true.
Any advice would be appreciated.
https://dl.dropboxusercontent.com/u/33103477/Q1.jpg
Homework Statement
There are a set number of marbles in a bag; the marbles consist of two colors. We are given the mean number of marbles of color 1 in the bag, as well as color 1's standard deviation. We are then asked to find the mean and standard deviation of color 2.Homework Equations
How...
Can you please help me find the density of the following functions?
The density of an absolutely continuous random variable X is:
fX(x) =
{ (3x^2-1)/12 if 1<x<2
{ 1/2 if 2<x<3
{ 0 elsewhere
Find the density of Y where Y = 4X-2
Find the density of M where M = (X-2)^2
Thank you!
Find cov(Y,Z) where Y = 2X_1 - 3X_2 + 4X_3 and Z = X_1 + 2X_2 - X_3
Information given E(X_1) =4
E(X_2) = 9
E(X_3) = 5
E(Y) = -7
E(Z) = 26
I tried expanding cov(Y,Z) = E(YZ) - E(Y)E(Z) but can't figure out how to calculate E(YZ)
(I wasn't sure how to title this, it's just that the statement resembles Chebychev's but with two RV's.)
Homework Statement Let \sigma_1^1 = \sigma_2^2 = \sigma^2 be the common variance of X_1 and X_2 and let [roh] (can't find the encoding for roh) be the correlation coefficient of X_1 and X_2...
Homework Statement
Let X_1, X_2, X_3 be iid with common pdf f(x)=exp(-x), 0<x<infinity, 0 elsewhere.
Evaluate P(X_1<X_2 | X_1<2X_2)Homework Equations
f(X|Y) = f(x,y)/f(y)
The Attempt at a Solution
Since P(X_1<X_2) is a subset of P(X_1<2X_2), the intersection (edited, at first said union)...
Hi,
I am struggling trying to find the (equation of the) pdf of the sum of (what I believe to be) two non-central chi-squared random variables.
The formula given on wikipedia (http://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution) shows that the random variable associated with...
Homework Statement
Two RVs X1 and X2 are continuous and have joint pdf
f_{X_1,X_2}(x_1, x_2) = \begin{cases} x_1+x_2 &\mbox{for } 0 < x_1 < 1; 0 < x_2 < 1
\\
0 & \mbox{ } \text{otherwise}. \end{cases}
Find the pdf of Y = X_1X_2.Homework Equations
I'm using the transformation "shortcut' that...
Homework Statement
Let us choose at random a point from the interval (0,1) and let the random variable X_1 be equal to the number which corresponds to that point. Then choose a point at random from the interval (0,x_1), where x_1 is the experimental value of X_1; and let the random variable...
Homework Statement
Homework Equations
Y=1/2*(X1-X3)^2+1/14*(X2+2X4-3X5)^2The Attempt at a Solution
For (a) part, I have only learned to find the moment-generating function of Y, but not finding the p.d.f.
Moreover, the examples I have seen only involves random variables Xi to the power 1, but...
Homework Statement
Three yearly losses.
First: Exponential
Second & Third: Weibull
Losses are independent.
Find the 95% VaR of the min loss
Homework Equations
The Attempt at a Solution
My first thought was:
Let L be total loss, A be first Loss, B be second loss, C be third...
i have a simple enough question
Find the MGF of a continuous random variable with the PDF:
f(x) = 2x, 0<x<1
I understand MGF is calculated as:
$$M(S) = \int_{-\infty}^{+\infty} e^{Sx} f(x)dx$$
which would give me
$$\int_{-\infty}^{+\infty} e^{Sx} 2xdx$$
but how would i compute this...
This is not a homework question but I project I am working on and need someone with more mathematical prowess than myself. I am using a computer program to draw random numbers from two independent distributions, x1 and x2, for two different cases and I want to establish a theoretical...
Are they always independent from each other so that you can multiply their E[X] together to form another E[X] with the same distribution and pmf or pdf?
Homework Statement
Given a sequence of independent random variables {X_n}, each one with distribution Exp(1). Show that Y_n = \displaystyle\frac{X_n}{\log(n)} with n \geq 2 converges to 0 in probability but it doesn't coverges almost surely to 0.
Homework Equations
Density for each X_n...
Hi all,
I would like to find the distribution (CDF or PDF) of a random variable Y, which is written as
Y=X_1*X_2*...X_N/(X_1+X_2+...X_N)^N.
X_1, X_2,...X_N are N i.i.d. random variables and we know they have the same PDF f_X(x).
I know this can be solved by change of variables technique and...
hello!
I'm trying to understand the following property:
Let X and Y be independent random variables z: = X + Y. Then
http://imageshack.us/a/img268/9228/71pe.png
where fZ (z) is the probability mass function for a discrete random variable defined as follows...
the random variables X1,X2... are independent and they take 0 and 1 values and they have expected value 0
if we have Y=X1+X2+...+Xn and Z=X1+X2+...+Xn+Xn+1 what is the ρ(Y,Z) for n=46
i know that ρ(Y,Z)=cov(Y,Z)/(sqrt(var(Y)*sqrt(var(Z)) but i need some help on how to find the cov and vars...
Hi,
Let's say I'm given X and Y identical independant continuous random variables.
We pose Z =X/Y, I remember there is a way to find the density function of Z, altough I can't get to remember how to do it and my probability book is out of town.(And I'm not so sure what to look for in google)...
Hello. I have a problem with probability theory task.
The task is:
X and Y is independent random variables with same density function fx=fy=f. What will be probability of P(X>Y).
This P(X>Y) reminds me a cdf: P(X>Y)=1-P(X<Y)=1-cdf of X.
Cdf of x is equal to integral ∫f dx from -inf to...
Let x(1),...,x(N) all be independent uniformally distributed variables defined on (0,1), i.e. (x(1),...,x(N)) - U(0,1). Define the random variable y(i) = x(i)/(x(1)+...+x(N)) for all i=1,...,N. I’m looking for the pdf of the random variables y(1),…,y(N). Has anyone come across such random...
Homework Statement
We have two independent, exponentially distributed random variables X and Y (with parameter a).
Z = X/(X+Y)
What is Z:s distributon function?
Homework Equations
The Attempt at a Solution
I think I need some intuition to what I'm really doing with these, I'm having a...
Homework Statement
Find correlation between random variables x and y in the following:
$$P_{x,y}(x,y)=A \ xy \ e^{-(x^2)}e^{-\frac{y^2}{2}}u(x)u(y)$$
Homework Equations
The co-variance ##\sigma_{xy}=\overline{(x-\bar{x})(y-\bar{y})}## or ##\sigma_{xy}=\overline{xy}-\bar{x}\bar{y}##...
I didn't post this in the probability section cause the questions I have are more regarded to communication system engineering.
I haven't actually been able to wrap my head around these concepts mainly cause all the study material I use have these really ambiguous explanations of each...
Hi everyone,
I have the following exercise.
Fx(x)=0, x<-1 or x>1
Fx(x)=1/2, x=[-1;1]
g(x)=x^2+1 --- this is the function of random variable
I must calculate Fy which is the sum of solutions of g(xk)=y , Fy(y)=sumFx(xk)/|g`(xk)|
g(x) is bijective on [-1;1]
y=x^2+1=> x=+sqrt(y-1) or x=-sqrt(y-1)...
Hi Everyone!
I have two normally distributed random variables. One on the x axis, the other on the y axis, like a complex normal random variable. I'm trying to find the pdf of the angle between a fixed point on the x-y plane(let's say point 1,0) and the vector formed by combining the two...
Oke this is a simple question but it has me a bit stumped.
Given a random variable X with a uniform probability distribution between [0,2].
What is the probability distribution function (pdf) of X^2 ?
Homework Statement
Let X and Y have the joint probability density function f(x,y)=k(1-y), if 0<x<y<1 and 0 elsewhere.
a)Find the value of k that makes this pdf valid.
b) Find P(X<3/4,Y>1/2)
c) Find the marginal density function of X and Y
d) Find the expected value and variance of X and...
Homework Statement
The joint PDF (probability density function) ##p_{X,Y}(x,y)## of two continuous random variables by:
$$ p_{X,Y}= Axy e^{-(x^2)}e^{\frac{-y^2}{2}}u(x)u(y)$$
a) find A
b) Find ##p_X (x), \ p_{y}, \ p_{X|Y}(x|y), and \ p_{Y|X}(y|x)##
Homework Equations
The first...
Homework Statement
A binary information source produces 0 and 1 with equal probability. The output of the source, denoted as X, is transmitted via an additive white Gaussian noise (AWGN) channel. The output of the channel, denoted as Y, satisfies Y = X + N, where the random noise N has the...
Classify the following as discrete or continuous random variables.
(A) The number of people in India
(B) The time it takes to overhaul an engine
(C) The blood pressures of patients admitted to a hospital in one day
(D) The length of a centipede
Homework Statement
Let X ~ Exponential(3) and Y ~ Poisson(5). Assume X and Y are independent. Let Z = X + Y. Compute the Cov(X,Z).Homework Equations
I know Cov(X, Z) = E(XZ) - E(X)E(Z). But how do I compute E(XZ) and E(Z) ?? Since for E(XZ), I would need the pdf/pmf (Exp is abs cts, while...
X and Y are independent, exponentially distributed random variables - with possibly different parameters
Determine the density func. of Z = X / Y
How to attack ?
Here is the question:
Consider the experiment of rolling two tetrahedra that are unfair in the sense that each has the following probabilities for each of the four faces:
P{1 dot}=1/10
P{2 dots}=2/10
P{3 dots}=3/10
P{4 dots}=4/10
Let X be the total of the outcomes in the two...
Homework Statement
Let X,W,Y be iid with a common geometric density f_x(x)= p(1-p)^x for x nonnegative integer
and p is in the interval (0,1)
What is the characteristic function of A= X-2W+3Y ?
Determine the family of the conditional distribution of X given X+W?
Homework Equations...
Homework Statement
f(x,y)= (4/5)(x+3y)exp(-x-2y) for x,y, >0
Find E[Y|X]
Homework Equations
E[Y|X] =integral y *f_xy (x,y)/ f_x (x) dy
The Attempt at a Solution
f_x (x) = integral [o,∞] [4/5](x+3y)exp(-x-2y) dx = (2x+3)/(5exp(x))
When taking the integral of y[(4/5)(x+3y)exp(-x-2y)] /...
Homework Statement
let y_1 and y_2 be iid bin(5,1/4) random variables
let v=y_1+2*y_2 and u = 3*y_1 -2y_2
find f_uv (u,v) and the cov(u,v)
Homework Equations
f_y (y) = (5 choose y) (1/4)^y (3/4)^5-x for x=0,1,2,3,4,5
covariance=E(uv)-E(u)E(v)
The Attempt at a Solution...
Suppose that α and β are independently distributed random variables, with means; μ_α, μ_b
and variances; δ_α^2, δ_β^2, respectively.
Further, let c=αβ+e, where e is independently distributed from α and β
with mean 0 and variance δ_e^2.
Does it hold that
E(αβ | c) = E(α|c)...
In the last question in this link:
http://pages.uoregon.edu/csinclai/teaching/Fall2009/files/hw8.pdf
1) I did not understand how they got the region for y1, y2, and y3...
2) How would the solution be different (or not possible) if X1, X2, and X3 were not iid?
Thanks in advance
We have two independent random variables X and Y whose pdfs are given as f(x) and f(y). Now when you multiply X and Y you get a random variable say Z. Now what is the resulting pdf f(z)?
I mean how is that related to the pdf of f(x) and f(y)?
From what I read it looks like
f(z)=f(x) *...
Hello
Let's say we have some continuous i.i.d random variables X_1, \ldots X_n from a known distribution with some parameter \theta
We then place them in ascending order X_{(1)}, \ldots X_{(n)} such that X_{(i)}, < X_{(i+1)}.
We call this operation T(\mathbf{X}) where \mathbf{X} is our...
Homework Statement
Take Ω = [0, 1] and P the uniform probability.
(a) Give an example of two random variables X and Y defined on Ω that
both have the same Bernoulli distribution with parameter θ = 1/3.
(b) Give an example of such random variables that are independent, and not
independent...
Homework Statement
The probability of being dealt a full house is approximately 0.0014. Find the probability that in 1000 hands of poker you will be dealt at least 2 full houses
Homework Equations
I can use binomial distribution.
The Attempt at a Solution
The probability of getting...
Homework Statement
I'm trying to show that U(X+Y) = X in distribution, where X and Y are independent exp(λ) distributed and U is uniformly distributed on (0,1) independent of X+Y.Homework Equations
The Attempt at a Solution
X+Y is gamma(2,λ) distributed. But I can't figure out how to deal with...
I have seen the following "extension" of discrete random variables definition, from:
pediaview.com/openpedia/Probability_distributions
(Abstract)
"... Equivalently to the above, a discrete random variable can be defined as a random variable whose cumulative distribution function (cdf)...