Example 5-50. Given the joint density function of X and Y as :f (x, y) = { 2x e-Y ; 0 < x < 2, y > 00 , elsewherefind the distribution of X + Y.

Answered: Image /qna-images/answer/b4f77fa8-fc6d-4493-a8b3-49a88a158ccc.jpg

Example 5-50. Given the joint density function of X and Y as : f (x, y) = {2*e*;0 0 , elsewhere find the distribution of X + Y,

Example 5-50. Given the joint density function of X and Y as : f (x, y) = {2e;0 0 , elsewhere find the distribution of X + Y,

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

ChapterA: Appendix

SectionA.2: Geometric Constructions

Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...

See similar textbooks

Related questions

Q: U is the universal set. A and B are subsets of U. n(U) = 30, n(A) = 13, and n(B) 12 n(A U B)' = 8 Sh...

Q: The probability that a contractor will get a plumbing contract, is 2/3 and the probability that he w...

A: Let P=a contractor will get a plumbing contractE=a contractor will get an electric contractGiven,P(P...

Q: 2. Suppose in a sample of size 10 articles, the probability that a single article will be nonconform...

A: Givensample size(n)=10The probability that a single article will be nonconforming (p)=0.1

Q: give at least 2 examples each of the different levels of measurement *nominal *interval *ratio *ordi...

A: Here we have to give two example of nominal ,interval ,ratio and ordinal

Q: Assume that a procedure yields a binomial distribution with a trial repeated n = binomial probabilit...

Q: In a trend and seasonality corrected exponential smoothing model explain what alpha, beta and gamma ...

Q: You are designing an IQ test where you aim for the average student to score at 100 IQ (that is not t...

A: Given that, 100 random sample are selected of third grade students in New Jersey. whose average sco...

Q: Find the quartiles of the Normal distribution having mean 60 and S.D 10.

Q: 4. A study was conducted to test diastolic blood pressure readings between patients with sedentary l...

A: The data of two groups A and B's diastolic blood pressure readings are given as: Group A Group B ...

Q: 8. You grow 20 crystals from a solution and measure the length of each crystal in millimeters. Here ...

Q: From the 457 business graduates of a university, 404 graduates consider to work after they have comp...

Q: Juanita makes $16 an hour at work. She has to take time off work to purchase her skirt, so each hour...

A: Given, Juanita is deciding whether to buy a skirt that she wants as well as where to buy it. Three s...

Q: At the beginning of each football season, the coaching staff at Vista High School must vote to decid...

A: Given Information: The voting system is {9: 8, 7, 1} Head coach A has a weight of 8, assistant coac...

Q: 6. A cooperative manager claims that the average daily income of the cooperative is P30,000 with sta...

Q: Consider the following survival tables relative two survival data of a clinical trial where survival...

A: @solution:: 1) SStotal is the Sum of Squares because of absolute Variation. It considers every on...

Q: Solve the Poisson equation Ди %3D — 4та, (х, у, 2) € (0, т] x [0, п] x [0, т], subject to the bounda...

A: Question:

Q: There are three math students (Ann, Kim and Billie) waiting for their turn to work with the math tut...

Q: In the most recent YouGov survey of 1,500 U.S. Adults Citizens, 39% said they approve of the job the...

A: @solution:::

Q: Problem #4 – The mean number of air conditioning units assembled per month by Freeze, Inc. is 750 an...

A: From the part 3-a, The variable cost is $400 per unit and monthly fixed cost of $200,000. If Freeze...

Q: Construct the simple linear regression equation of Y on X if n = 7, Ex,=113, E =1983, -182 and =3186...

Q: In a factory there are 100 skilled, 250 semi-skilled and 150 unskilled workers. It has been observed...

A: Given : There are 100 skilled, 250 semi-skilled & 150 unskilled workers on an average a unit is...

Q: 90% confidence interval for the difference in mean number of species between unlogged and logged plo...

A: Given: Unlogged forest: 22 18 22 20 15 21 13 13 19 13 19 15 Logged forest: 17 4 18 14 18 15 15 10 1...

Q: A doctor has decided to prescribe two new drugs to 200 heart patients, as follows: 50 get drug A, 50...

A: Let assume P(DA) = Probability of patient having Drug A P(DB) = Probability of patient having Drug ...

Q: Two types of batteries are tested for their length of life (in hours). The following data is the sum...

Q: Your boss wants you to sample a small number of parts from a large order to be able to guarantee 0 d...

A: Your boss wants you to sample a small number of parts from a large order to be able to guarantee 0 d...

Q: A hotel has 50 "luxury" rooms and 250 "regular" rooms. On a given night, the demand for luxury rooms...

A: @solution::: We can mimic this issue in R utilizing rpois and dbinom capacities from the details lib...

Q: If a can is selected randomly, calculate the probability of getting: a) a defective can; b) a good c...

A: Let us define some events A : a can coming from line A B : a can coming from line B C : a can comin...

Q: 2.10 Guessing on an exam: In a multiple choice exam, there are 6 questions and 4 choices for each qu...

Q: mean life span of the bulbs is significantly different from 2000 hours.

A: Here sample mean = 1950 Sample size = 100 and Population standard deviation = 150 Here Population...

Q: Home Saved CICI LU UIC uI UCIC LUCIUN. FRONT PAGE College Tuition Up Again College gets more expensi...

Q: A 95% confidence interval for the mean m of a population is computed from a random sample and found ...

A: As per Bartleby guideline expert have to answer first question only dear student please upload other...

Q: Which of the following is a discrete random variable? o a the length of time spent in reading lesson...

A: Disclaimer : Since you have asked multiple question, we will solve the first question for you. If yo...

Q: For the data 69.65, 69.63, 69.64, 69.21. Calculate the 95% confidence limit.

A: Given data is69.65,69.63,69.64,69.21Confidence interval is

Q: Construct a 95% confidence interval for the mean difference in calcium levels in the soil prior to a...

A: Q.1)

Q: Two balls are drawn in succession without replacement from a box containing 7 red balls and 12 balls...

A: Given, Two balls are drawn in succession without replacement from a box containing 7 red balls and 1...

Q: 20. Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug zopi- cl...

Q: Consumer: Radon Gas “Radon: The Problem No One Wants to Face" is the title of an article appearing i...

A: Given data 1.9, 2.8, 5.7, 4.2, 1.9, 8.6, 3.9, 7.2 and n=8 Here we have to interpret that based o...

Q: List the elements of each of the following sample spaces:

A: sample space is set of all possible outcomes

Q: There are four blood types, and not all are equally likely to be in blood banks. In a certain blood ...

A: In certain blood bank, there are four types of blood which are not equally likely to be available in...

Q: Find the probability. A spinner has an equal chance of landing on each of its seven numbered regions...

A: The probability of an event is calculated by dividing the favorable number of outcomes by the total ...

Q: Find , o, 0z' for all possible samples of 187 values taken from a Normally distributed population wi...

A: Given mean is 66.34 and standard deviation is 44.02.

Q: Frank Catton, the general manager of Billybob's floating raft hotel and casino in Tunica Mississippi...

Q: Find the probability distribution for the number of heads that occur when 4 coins are tossed.

Q: 2. Suppose that we are doing batch testing with batches of size 12. Suppose that the probability tha...

A: It is given that the size of the batches is 12 and probability that a batch test negative is 0.655.

Q: The spending in dollars of 26551 customers in one marketing segment of a credit card company, during...

A: Given, The spending in dollars of 26551 customers in one marketing segment of a credit card company ...

Q: The American Association of Individual Investors (AAII) On-Line Discount Broker Survey polls members...

A: Disclaimer : “Since you have posted a question with multiple sub-parts, we will solve first three su...

Q: In a certain country the heights of adult men are normally distributed with a mean of 68.9 inches an...

Q: Activity 2 Let X be a hypergeometric random variable with N = 15, n= 4, and k = 5. %3D Calculate the...

Q: A probability based on equally likely outcomes is called a __________ probability.

Q: Example 5-35. A two-dimensional r.v. (X, Y) have a bivariate distribution givenm by : x2 + y P (X = ...

Question

100%

Example 5-50. Given the joint density function of X and Y as :
f (x, y) = { 2
x e-Y ; 0 < x < 2, y > 0
0 , elsewhere
find the distribution of X + Y.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.
endent. 3.60 The joint probability density function of the ran- dom variables X, Y, and Z is ry=", 0 }, 2 < Z < 3); (d) P(0 < Z < 2 | X = , Y = }). 75°F Mostly cloudy
24. Consider a distribution with density on the interval [0, 2]. Let the probability density function (pdf) for this distribution be the following: fy(u) = % on [0, 2] 2 (i) Draw/plot the pdf fy(y) vs. y for the interval [0, 2]. (ii) Determine the Cumulative Distribution Function (CDF), F, (y). (iii) Draw/plot the CDF F,(y) vs y for the interval [0, 2]. (iv) Determine the expected value of the Random Variable (RV) y, i.e., E [y].
Let X be the concentration of ethanol in chemical solution and Y be the acidity of the solution, Suppose the joint probability density function of these two variables is given by (picture as below) i. the value of the constant C. ii. the marginal probability density functions of fx(x) of X and fy(y) of Y
asysb, If the density function of Y is f(y)={ b-a' 0, Otherwise. then the variance of Y is equal to Select one: (b-a) a. 12 (a+b? Ob. 12 a+b
The probability density function of X is given by the following table: X 2. 3 4 5 P(x) K 3K 5K 7K 9K 11K 13K Find (i) P (X 0.3 ?
4. Let X and Y be random variables. The density function of X is 1 | 24x²;0 < x <: 2 ; f (x) = - 0; elsewhere The conditional density of Y given X = x is y 5;0 < y < 2x g(y/x) ={2x? 0; elsewhere What is the form of the marginal density function of Y where it is nonzero?
Suppose that X and Y have a joint probability density function given by ce-3z=5y if a, y 20 fx.y(T, y) = otherwise Find the marginal probability density function fx and state the name of the distribution of X.
c) Let S and T be two independent random variables with probability density functions 1 f(s)= - s > 0, e elsewhere. (e) = t > 0, e 0. elsewhere. Given X = S+ Y and Y = T. Find a joint probability distribution function of X and Y. Then determine the marginal density function of Y.
1. Let X and Y have joint probability density function (pdf) given by 1,0 < x₁, x₂ <1, elsewhere. 0, Also find the marginal density functions of Y and Y₂₁. f (x₁, x₂) = Find the joint probability density function of Y₁ = X₁ + X₂ and Y₂ = X₁ X₂.
p(x) represents the probability density function of variable x. Four samples of delta function are located at x = 1, x = 2, x = 3 and x = 4 as shown in figure below. Area of each delta function is given by p(x) 1 2 3 4 a) 1/2, 1/2, 1/2, 1/2 b) 1/3, 1/3, 1/3, 1/3 c) 1/4, 1/4, 1/4.% d) 1/5, 1/5, 1/5, 1/5
3. If a dealer's profit, in units of $5000, on a new automobile is a random variable X having the density function f(x)= 2(1-x), 0 < x < 1, zero elsewhere, find the average profit per automobile.