Answered: Help please: Let X1, X2, . . . , Xn be…

Help please: Let X1, X2, . . . , Xn be i.i.d. from a uniform distribution over the interval (0, 1). Let Y = max{X1, X2, . . . , Xn}. Show that the PDF of Y has a Beta distribution.

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Exponential And Logarithmic Functions

Section5.5: Exponential And Logarithmic Models

Problem 4ECP

See similar textbooks

Related questions

Q: 1) For simple random samples of size n = 30, determine the mean of the sampling distribution of x,…

A: Based on your reasoning the location of the second hand of a clock when the teacher walks through…

Q: 12. Use the following information and answer the next two questions: The Journal of Finance…

A: The total number of adults in the sample is 158,044.

Q: Find the indicated z-score shown in the graph to the right. The z-score is. (Round to two decimal…

A: The given area is 0.0735.

Q: 10

A: It is given that the square of side 10 and the radius of the circle is half of the sqaure.

Q: 4.1. Suppose X and Y are independent random variables, which are jointly continuous. 1. Show…

A: Suppose X and Y each have an exponential distribution with parameter .

Q: The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year…

A: μ=3.28,σ=0.18

Q: er of yes answers on a questionnaire called the Hooked on ne Checklist (HONC). Of teenagers who had…

A: Sample sizes n1=141 ,n2=178Sample means x1=3.8 ,x2=2.4

Q: Industry A is responsible for producing 60% of cements in Lebanon while Industry B produces the…

Q: Based on an analysis of sample data, an article proposed the pdf f(x) = 0.55e-0.55(x - 1) when x 2 1…

A: Let X be the time spent at the median line.Given that, the pdf of X is

Q: 3.1 Repeat observing a distance for n times with independent equal weight. Please proof that the…

A: To prove that the most probable value (MPV) of the observations is the direct mean by the Least…

Q: You're a contestant on a TV game show. In the final round of the game, if contestants answer a…

A: You're a contestant on a TV game show. In the final round of the game, if contestants answer a…

Q: Problem 4: A finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine…

A: Given that a finite state machine has 3 states, labeled {1, 2, 3}. The input of this state machine…

Q: When three friends go for coffee, they decide who will pay the check by each flipping a coin and…

A: The distribution follows a Geometric distribution (i.e. )The total number of outcomes (i.e. three…

Q: Question 3 Calculate the probability of getting 3 hearts when you draw 5 cards; that is, calculate…

A: We have to draw cards from a standard deck of cards.i.e. Let, be the number of cards drawn. be the…

Q: Consider the random movement of a bishop on a chessboard (look up the definitions on the…

A: In the random movement of a bishop on a chessboard, we can model the bishop's movement as a Markov…

Q: builtrite has calculated average weekly daily sales to be 80000 with a standard deviation of 12000.…

A: Mean()=80000standard deviation()=12000 one store manager made a bet with another store manager that…

Q: how many ways can first second and third prizes be awarded in a contest with 530 contestants?

A: To determine the number of ways to award first, second, and third prizes in a contest with 530…

Q: Consider a signal detection problem involving two hypotheses: H₁ : X = W and where H₁ : X = 8 + W,…

A: Where is a known signal vector and is a vector of independent Gaussian random variables with mean…

Q: In each case, determine the value of the constant c that makes the probability statement correct.…

A: c=constantZ be the standard normal distribution. Note: According to the Bartleby guidelines experts…

Q: For an experiment, roll 2 fair dice. Let the random variables, X = sum of the 2 dice Y = larger…

A: For an experiment, roll 2 fair dice.Let the random variables, X = sum of the 2 dice Y = larger value…

Q: The sample space contains 9 As and 7 Bs. What is the probablity that a randomly selected set of 3…

A: Let total number of sample space=9+7=16(9A+7B) From 16 samples we want to select 3 samplesTherefore,…

Q: (a) Let C denote the time when the room goes dark. Find the pdf of C. b) What is E[C]? Hint: the pdf…

A: Given,A room is lit by two light bulbs bulbs which are connected in series circuit. if either light…

Q: A machine can be in one of four states: ‘running smoothly’ (state 1), ‘running but needs adjustment’…

A: The idea is to describe plainly the event that is given in the form of a mathematical…

Q: You went to a clinic to visit the doctor. There were 4 patients ahead of you in the waiting room.…

A: Given that there are 4 patients ahead in the waiting room. Their waiting times to meet the doctor…

Q: Find the indicated z-scores shown in the graph. Click to view page 1 of the table. Click to view…

Q: If X is a binomial random variable and if np≥ 10 and n (1-p) ≥10, then X is approximately normal…

A: Given that X is a binomial random variable.If np>=10 and n( 1-p) >= 10,>=10, then X is…

Q: (c) An insurance company has observed the number of accidents that an individual has suffered on…

A: (c)Given, follows a gamma distribution with shape parameter are independent random variables ,each…

Q: Ten applicants applied for jobs in a company. The review process has three stages. The company first…

A: In this first stage, the probability that an applicant is not rejected at this stage is 0.5. The…

Q: In the following problem, check that it is appropriate to use the normal approximation to the…

Q: cards 3. Select five cards without replacement from a deck of cards/Let X be the number of heart…

A: 3)Here given that, we have to select five cards without replacement from a deck of cards.Let, X be…

Q: c. Using Emily's sample results, construct a 90% confidence interval estimate of the proportion of…

A: The best point estimate of the therapists success rate is 0.481.

Q: Problem 2. Exponential Distribution. A factory has a set of 10 machines. Each of these machines will…

A: Given that the failure time T of the machines is exponentially distributed with parameter λ=2,…

Q: There are 8 balls of which 2 are white and 6 red. For the first time, 2 balls are taken from the…

A: Total balls = 8 White balls = 2 Red balls = 6 First time : 2 balls are taken from the bag Than 2…

Q: According to a university's report, only 35% of all surgical operations at that time required an…

A: Given,The percentage of surgical operations requiring an overnight stay at a hospital is = 35%.So,…

Q: Find the sample size needed to estimate the mean age of movie patrons such that it can be said with…

Q: Let X denote the proportion of allotted time that a randomly selected student spends working on a…

Q: The number of errors per 1000 words made by a particular typist has a Poisson distribution with a…

A: From the information, given thatLet X denotes the number of errors per 1000 words made by a…

Q: There are 5, 673 students enrolled at the University of New Mexico Suppose I as each one of them to…

A: Given that there are 5673 students.Suppose I ask each one of them to pick a number between 1 and…

Q: Consider the following transition probability matrix: [0.6 0.2 0.2 P= 0.3 0.4 0.3 0.0 0.3 0.7 a.…

A: transition probability matrix is given:

Q: The diameters of a large group of gravel particles follow a normal distribution with mean diameter…

A: From the provided information,

Q: Consider the following discrete probability mass function. X 0 P(X= x) 3 0.25 1 0.30 Find P(1 < X <…

A: The discrete probability mass function is:x31-1P(X=x)0.250.300.45

Q: A bag contains 9 Cherry Starbursts and 21 other flavored Starburts. 10 Starbursts are chosen…

A: There are total 9 cherry starbursts and 21 other flavoured starbursts.

Q: The sale price of a certain model of grand piano across the country is approximately normally…

A: Let X denotes the sale price of a certain model of grand piono with mean = $86000 and standard…

Q: Imagine you have a bag containing 5 red, 3 blue and 2 orange chips. If drawing without replacement,…

A: Given,Number of red chips, n(red) = 5Number of blue chips, n(blue) = 3Number of orange chips,…

Q: Let the joint density function of random variables (X, Y) be f(x, y) = -2x-3y (Ae ²x-³y, x>0, y>0 0,…

A: Given the joint density function of random variables :

Q: K One of the major products at a large company is french fries that are sold on the commercial…

A: P=0.09n=400X=48

Q: 4. The port authority has denied the shipment of the cargo ship from China to Malaysia due to…

A: Given the standard size of the 20 foot container according to ISO 668:2013 is . The sample for 10…

Q: Find the z-score that has 3.851% of the distribution's area to its left. The Z-score is (Round to…

A: The formula of the Z-score is,Where,X denotes the raw data point, µ denotes the population mean,σ…

Q: Problem 10-17 (Static) An office employs several clerks who create documents and has one operator…

A: In this system population is infinite, arrivals are poisson distributed and service time is…

Q: day. Which probability distribution is most nearly appropriate to describe the number of dog bite…

A: It is assumed that the random variable represents the number of dog bite victims.

Question

Help please:

Let X1, X2, . . . , Xn be i.i.d. from a uniform distribution over the interval (0, 1). Let

Y = max{X1, X2, . . . , Xn}.

Show that the PDF of Y has a Beta distribution.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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: Determine the given variable

VIEW

Step 2: Determine beta distribution

VIEW

Solution

VIEW

Step by step

Solved in 3 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Can the average rate of change of a function be constant?
Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.
Let X ~ I(2,B). Find the distribution of Y = 2X.
Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.
(26) Let X b(8,- Var-x) and distribution function.
Varza) (16) Let X =U(3) find x) and distribution function.
Let X ~ U[0,1] and Y = -βln(1-X). What is the distribution of Y? Justify.
Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distribution
(3) Let X = b >(8,-) find E(5+6x) and distribution function.
A function has a graph which passes through the point (2,3) and its graph also has the property that the normal line to each point (x,y) on the graph passes through the point (2,0). Find the function?
Let Y > 0 be a continuous random variable representing time from regimen start to bone-marrow transplant. Everyone does not survive long enough to get the transplant. Let X > 0 be a continuous random variable representing time from regimen start to death. We can assume X ⊥ Y and model time to death as X ∼ Exp(rate = θ) and time to transplant as Y ∼ Exp(rate = µ). Where Exp(rate = λ) denotes the exponential distribution with density f(z | λ) = λe−λz for z > 0 and 0 elsewhere - with λ > 0. Find the probability that the patient would die before receiving transplant.