→5)Two random variables X and Y are distributed according tofx,y(x, y) = {K(x+y),0≤x,y≤1otherwisea) Find K.b) What is the probability that X + Y > 1?c) Find P(X > Y).d) What is P(X > Y | X + 2Y > 1)?e) Find P(X=Y).f) What is P(X>0.5| X = Y)?g) Find fx (x) and fy (y).h) Find fx (x|X + 2Y > 1) and E(X|X + 2Y > 1).Please select two IEEE Magazine articles about one of the following topicsdetermined according to the last digit of your school ID and prepare a detailed report:Last Digit0 & 12 & 34 & 56 & 78 & 9TopicTerrestrial TV BroadcastingFM Broadcast RadioPublic Switched Telephone Network1st Generation Cellular System2nd Generation Cellular SystemYour report should include answers of the following questions for each article and it shouldconsist of at least 600 words in total.a) What are the title of the selected articles? State the names of the authors.b) What are the main topics of the articles? State the problem discussed in the articles.c) Explain the selected method/methods for solving the problem in the articles.d) Explain three main observations & comparisons about the selected method/methods.

Given, continuous probability density function.Concept:We know that total ofallthe probability…

Answered: 4) Two random variables X and Y are…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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K 2) d) Find the value of t and p if P(t t) : = 3) Suppose that X~x²(v) and Y~x²(n). If µx = 6, o²y = 16 and W a) State with parameter(s) the distribution of W. 4X 3Y Ơ V = then
11 the probability distribution of discete random variable x is given by p (X=x) = k÷ x+1 for x = 1,2,3 a) find the value of K where K is constant b) compute P(x=2) C) compute p(x=2 or x=3)
There are two boxes. In each box there are 4 cards with a different number printed on it. The four cards have been numbered as 1,2,3,4 in each box. Two cards are drawn random from each box. The random variable X represents the difference between the number on the card from box 1 minus the number on the card from box 2.a) Find the mean of this probability distribution. (i.e. Find E[X] )b) Find the variance and standard deviation of this probability distribution.(i.e. Find V[X] and SD[X])The random variables M and W are defined as follows:M = X+5 and W = (1/2)X+5c) Find E[M] and E[W].d) Find V[M] and V[W].e) Mary and William play a game using the cards in the above boxes. Randomly two cards are drawn, and Mary records his score using the random variable M and William uses the random variable W. They repeat this for a large number of times and compare their scores. Comment on any likely differences or similarities of their scores.
Determine the distribution of the random variable X and sketch its graph. for a E (-00, -1) x € [-1, }) for e € [},2) 品 for for a) F(x) = x € [2, ) æ € },+) 17 20 for too) 1
6- The Variance of X, is a) o? b) d) 2
If X and Y are independent RVs, each following N (0, 3), what is the probability that the point (X, Y) lies between the lines 3X + 4Y = 5 and 3X + 4Y = 10?
Suppose that one variable, xx, is chosen randomly and uniformly from [0, 1], and another variable, yy, is also chosen randomly and uniformly from [0, 2]. What is the probability that x≤y≤2x+1x≤y≤2x+1?The probability for x≤y≤2x+1x≤y≤2x+1 is?
D5) X and Y are two points that are selected according to a uniform distribution. Calculate the expected value of the distance between these two points for each of the following cases: a) Both X and Y are selected independently from the range 0-1. b) We select X between 0 and 1 and then select Y between 0 and X. Note: For case b the distance is equal to |Y-X|
1) If X~ N(100,49), find the probability P(X> 107)
point) Four buses carrying 157 high school students arrive to Montreal. The buses carry, respectively, 33, 50, 25, and 49 students. One of the studetns is randomly selected. Let X denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on his bus. Compute the expectations and variances of X and Y: E(X) = Var(X) = E(Y) = Var(Y) =

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