Random variables Definition and 318 Threads

Hi, What is meant by "convergence of random variables"? Specifically, this statement confuses me: The sequence of random variables X_1, X_2, ... , X_n is said to converge in probability to the constant c if for any \epsilon > 0: \lim_{n \rightarrow \infty} P(\vert X_n - c \vert <...

Suppose I had n random variables, all of which have the same distribution but different mean and variances. How can I formally describe the distribution of these n random variables.

A multiple choice test contains 12 questions, 8 of which have 4 answers each to choose from and 4 of which have 5 answers to choose from. If a student randomly guesses all of his answers, what is the probability that he will get exactly 2 of the 4 answer questions correct and at least 3 of the 5...

Since I am noob in LaTex then ill post a document in Word.

I have been working on this problem and can't seem to get the answer. Problem: X is a continuous random variable with a proabaility density function: f(x) = 1/4 if -2<=x<=2 0 other wise Let Y=1/X. Then P(Y<=1/2) = ? This is how I approached the problem...

Let S={1,2,3,4,5,6}, F=σ(A1,A2), ie., the σ-algebra generated by A1 and A1 (the smallest σ-algebra containing A1 and A2) with A1={1,2,3,4} and A2={3,4,5,6}. Please complete the following: a. List all sets in F b. Is the random variable X(w)= 2, w=1,2,3,4; X(w)=7, w=5,6 measurable w.r.t. F...

I've been working on a problem and was wondering if someone could check and see if I am on the right track. A company produces gas from two plants, A and B. (both are considered to be continuous randm variables; X and Y respectively) For Plant A, its probability density function is...

anyone's help would be really appreciated. I can't figure out that one. If X and Y are joint random variables, what is the joint distribution funtion of U=min(X,Y) and V=max(X,Y). I got something like 2[u(v-u) + ½u^2)] then how do i worked towards and expression for the marginal...

Hi I'm wondering if someone can help me out on this question as to how to go about doing it: X_1, X_2... X_7 are independent random variables represnting a random sample of size 7 from the normal N(10, 7) distribution. Find to 3 dp probablitity that the sample total exceeds 88. I tried to...

I have a question about independent random variable: Let say we flip a fair coin, the set of outcome is S={H,T}, P(H)=1/2, P(T)=1/2. Define random variable X:S->R by X(H)=1, X(T)=-1. From what I read in books, I can define X1 and X2 as independent identically distributed (iid) random variables...

How do you show that a linear combination of two Gaussian Random Variables is again Gaussian?

Hi, I really need help with joint PDF, if anyone can help, that would be super! :smile: Random Variables X and Y have joint PDF fx,y (x, y) = 1/2 if -1 <= x <=y <= 1, and it is 0 otherwise a) what is fy (y)? b) what is fx|y (x|y)? c) what is E[X|Y = y]?

Hi I need some help. I don't think I did any of this right. A small business just leased a new computer and color laser printer for three years. The service contract for the computer offers unlimited repairs for a fee of $100 a year plus a $25 service charge for each repair needed. The...

Hello (first time poster), i am having quite a bit of trouble with a particular problem on stats (which i despise of!) - in particular, discrete random variables.Ok here is the question: "Find the probability distribution of X in each of the following questions ... Two fair dice...

I hope someone can help me understand functions of random variables: If X~Uniform(A,B), A < X < B Y~Normal(0,1), -inf < Y < inf and Z = X + Y - what is the pdf of Z? - how can I calculate a probability like P(Z < 3)? - what is the conditional probability P(Z<z | X = x)? - what is the...

Hello, I need some help on the independence of random variables... "How do I prove that if X and Y are two independent random variables, then U=g(X) and V = h(Y) are also independent?" - Isn`t that if random variables X and Y are independent, it implies that f(x,y) = g(x)h(y) and vice...

Consider the experiment of tossing a die thrice. X is defined as the number of different faces that appear (i.e., X = 1,2,3). What is meant by the "number of different faces that appear"? Could you help me how could I get P(X = 1,2,3)?

I have two questions.. any insight into either of them is appreciated. 1) A fair coin is tossed repeatedly; the sequence of outcomes is recorded. Let Y be the random time of the first appearance of HT (a tail immediately following a head). (a) Find P(Y = 4): (b) Find E[Y] (the expected...