cdf

1. Calculating Cauchy's PDF, using domain definition drawings of F_X/Y(z)

Hi, I am trying to draw F (CDF of Cauchy) using X/Y relation for X,Y~N(0,1) iids and at some point very shortly I get lost. Especially because I don't know if I'm on the right direction. Could you direct me to the right way of solving this using the way I chose? So. Problem: Given X,Y~N(0,1)...

A firm produces chains. The length of each link is independent of each other and normally distributed. The mean length of a link is 10. 95% of all links have a length between 9 and 11. The total length of each chain is the sum of the lengths of its links. You consider chains with 100 links 2...
3. Minimum CDF of non-independent random variables

How can I find the CDF for F_{X,Y}={x,x} if X,Y are not-independent. In other words, what will be Pr{min(X,Y)<x} if X,Y are not-independent? If I already know the individual CDF of both X and Y, i.e. F_{X}(x) and F_{Y}(x), can they be useful to compute the Pr{min(X,Y)<x}, where X,Y are...
4. Trying to calculate confidence intervals

Hi everyone. The numbers below are the annual maintenance costs of a program I am working on. I'd like to use the data set to estimate future costs at different confidence intervals (e.g. 80%). Can you help me with what distribution would be best and how to produce a CDF that I can graph...
5. Getting a cdf equal to 1 from a variable kernel density estimation

When I integrate the variable kernel density estimation of a sample from -inf to inf, I should get 1. But it is not what I get with my code below. I find a value higher than 2. How can I fix this? n<-1000 df <- data.frame(x=unlist(lapply(1, function(i) rnorm(n, 0,sd=1))))...
6. CDF of average

Hi all, I hope that someone can help me with this! I have a list of values as below: 82.1134 84.5516 91.1851 65.6035 69.971 92.4706 79.1505 93.0844 92.9598 and I need to find the CDF of their average! how can calculate and present that in a chart? :confused: I do appreciate any...
7. Cumulative distribution function (cdf) - empirical vs theoretical ?

Hello to all, I have a data-set with n = 90, probably follows the gamma distribution. I used the maximum-likelihood estimation (MLE) to estimated the alpha and beta parameters of the gamma distribution using Matlab. My question is What is the best way to test the fit (goodness of fit) of the...
8. Help verifying a CDF is actually a CDF

Hello All, First post here so thank you for reading and hopefully helping out! I'm feeling stumped with this first question and was hoping someone could help point me in the right direction. I understand, at least I think I do, how to to find the actual probabilities for part b) i, ii and iii...
9. Proof the sum of two CDF's is a CDF.

This is a question my instructor asked in the last midterm exam but nobody was able to solve and he's suggesting it may come out again in the finals: If F(x) and G(X) are two CDF's, prove that H(X) is also a CDF if H(X) = F(X)+G(X)-F(x)G(X) He said something about right...
10. Help with cdf

I'm having trouble with grasping cdf's. If I have a cumulative distribution function F(x) = .0 ----- x<-2 .2 ----- -2 ≤ x< 0 .5 ----- 0 ≤ x < 1 .7 ----- 1...
11. Deriving Var from mu and two Ps

If I know the mean of a normal distribution and two probabilities F1=P(Z>z1) and F2=P(Z>z2), I should be able to derive the Var of the distribution, no? Can't figure how. Do I need to manipulate the CDF algebraically, or is there an easier (non-calculus intensive) way? In real terms, I know...
12. PROC IML module for CDF

How would one create a proc iml module to calculate the cdf? Denote f(x;μ,σ) and F(x;μ,σ), respectively, the p.d.f. and the c.d.f. of N(μ,σ^2). The p.d.f. and the c.d.f. of contaminated normal cN(μ,σ2,σc^2,p) (a N(μ,σ^2) contaminated in spread by a N(μ,σc^2) with probability p) are...
13. SAS: cdf for contaminated normal (PROC IML)

Denote f(x;μ,σ) and F(x;μ,σ), respectively, the p.d.f. and the c.d.f. of N(μ,σ^2). The p.d.f. and the c.d.f. of contaminated normal cN(μ,σ2,σc^2,p) (a N(μ,σ^2) contaminated in spread by a N(μ,σc^2) with probability p) are (1-p)f(x;μ,σ)+pf(x;μ,σc) and (1-p)F(x;μ,σ)+pF(x;μ,σc), respectively...
14. Finding a PDF using the CDF technique

Hey guys, I'm stuck on a question in my homework assignment and I was wondering if you could push me in the right direction? So here's the question: X and Y are continuous random variables with joint pdf f(x,y)= 4xy (0<x<1, 0<y<1, and otherwise 0). Find the pdf of T=X+Y using the CDF...
15. Help with the Continuous Distribution Function (CDF)?

Hey, new to these forums, I was wondering if you guy could help me with a question about the CDF I have. Basically I'm wondering if this CDF: G(t)= {0 , t<0 t^2 , 0<=t<1 t , 1<=t<2 1 , t>=2 } The same as this one: G(t)= {0 , t<0 t^2+t , 0<=t<2 1 , t>=2 } ? Thanks...
16. cumulative distribution function of a uniform distribution

I just need some help on the question below. Bacteria are grown in a dish for a length of time (in hours) T which is a random variable with a uniform distribution over the range 5 to 6; that is, it has the pdf F(t) = {1, 5<= t <=6} {0, otherwise} the number of bacteria Y, in the dish...
17. Order Statistics Problem

Hi there I have random variables X1,X2,X3,...,XN which are I.I.D. Each of these random variables are Erlang Distributed. X=min{X1,...,XN}. Now the sample size N changes with each iteration according to the following rule If Yn<=X<Yn+1 Then N=2^n where n is an element of...
18. Functions of Random Variable.

Let X be exponential(lambda), and let Y=max(1,X). Find the cdf of Y. Also sketch the cdf. Suppose that X is discrete with pmf p(0)=p(1)=2p(2) (and zero otherwise). Find the pmf and cdf of X. How would you simulate the random variable X starting with U, a uniform[0,1] random variable? That is...
19. Joint and Marginal Densities.

I am having some problems grasping the concept of these joint and marginal densities. It would really help if someone could provide me with an answer for the following question: Find the joint and marginal densities corresponding to the cdf F(X, Y) = (1 - е^αx){1-e^βy), x > 0, y>0, α >...
20. PDF Stats =/

The number of vehicles leaving a turnpike at a certain exit during a particular time period has approximately a normal distribution with mean value 400 and standard deviation 75. Determine the proabilities below. (Round all answers to four decimal places.) (a) What is the probability that...