Answered: Let X be a continuous uniform random…

Let X be a continuous uniform random variable on [a, b]: X ~ U[a, b]. a Write down the pdf and cdf of X. b Calculate the expectation and the variance of X.

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...

See similar textbooks

Related questions

Q: Classify the variable as qualitative or quantitative. If quantitative, classify further as discrete ...

A: Here use basic of qualitative and quantitative

Q: A brokerage firm has two types of clients, those who prefer high-risk portfolios and those who prefe...

A: Introduction: A client has two options regarding using leverage- either they use leverage, or they d...

Q: Consider the visits that result in leave without being seen (LWBS) at an emergency department in the...

A: From the help of above given table we need to answer certain questions.

Q: If four children's books in the category of fantasy fiction, two in the category of fairytales, and ...

A: Here AS PER POLICY I HAVE CALCULATED FIRST MAIN QUESTION Mr. de Mesa has fifteen different children...

Q: Let us assume that the game company has designed a guarantee mechanism to encourage users to pay for...

A: Note :- as per bartleby guidlines i have solved part off first part only. Please post again if u wan...

Q: 13. Let X equal the number of widgets that are defective when 3 widgets are randomly chosen and obse...

Q: Four cards are drawn successively with replacement from the well-shuffled deck of 52 cards what is t...

A: Solution:

Q: 1A. Check if numbers 1, 2, 3, 5, 4, 5 can represent lengths of a prefix code. Prove. 1B. The alphabe...

A: we are solving this problem by means of Huffman code with minimum variance below are the steps to fo...

Q: - Find a 95% confidence interval for p1 - p2.

A: Here use confidence interval of difference of proportion

Q: Suppose a computer company has manufacturing plants in three states. 50% of its computers are manufa...

Q: There is a standard deck of 52 cards, a hand of 7 is dealt. Please find How many hands are possibl...

A: Since the deck of cards consists of 52 cards we can say that the total possible outcome for each car...

Q: F(x) Let X be a continuous random variable with cdf F(x). Show that E(I(X < r)) where I is the indic...

Q: TOPIC: Permutation / Combination There are 2 red Toyota, 3 black Honda and 4 white Mitsubishi cars ...

Q: In the midst of labor–management negotiations, the president of a company argues that the company’s ...

A: Given information: Use the given data to determine the mean, count, sum and standard deviation using...

Q: If S= {0,1,2,3,4,5,6,7,8,9} ve A={0,2,4,6,8}, B={1,3,5,7,9}, C={2,3,4,5} and D= {1,6,7}, list the el...

A: The sample space is denoted by S and it is the complete set of all the possible outcomes of the expe...

Q: 6. 4 married couples bought 8 seats in the same row for a concert. How many different ways can they ...

A: 4 married couples bought 8 seats in the same row for a concert ( a) without restriction ? (b ) If ea...

Q: 13. A supplier delivers an order for 30 electric toothbrushes to a store. By accident, three of the ...

Q: 11. In a management trainee program, 80% of the trainees are female, while 20% are male. Ninety perc...

Q: Example 3.9. For x = 1,2 and y = 1,2, let the joint PMF of X and Y be defined by ry fx.y(x, y) = 15 ...

Q: Among the products of the first company, defective is 10%, the second 20%, the third 25%. We bought...

A: The probability that an event occurs, is equal to ratio of number of favourable outcomes for the eve...

Q: There are two series of index numbers, P for price index and S for stock of a commodity. The mean an...

A: Solution is given. Hope the answer is helpful.

Q: During periods when the unadjusted federal minimum wage is constant identify the trend .

A: The minimum wage needs to be fixed based on Employment growth rather than employment levels. The obs...

Q: The number of customers waiting for gift-wrap service at a department store is an rv X with possible...

A: In this case, we can observe that the two events are not independent. The variable X represents the ...

Q: Two different teams named A and B are asked to separately design a new product within a month. From ...

A: just look at the Venn- Diagram............

Q: Heart failure is due to either natural occurrences (84%) or outside factors (16%). Outside factors a...

Q: When a single die is rolled, find the probability of getting a 7.

A: It is a problem of basic probability in which we have to find out the probability of getting a 7.

Q: A. Given a standard normal distribution, draw, find the area and write the probability notation. 1. ...

A: Given that, Mean, u= 8 And standard deviation= 2 It is known that, z-score= (x-u)/standard deviatio...

Q: 4. (a) Consider a nonnegative, integer valued random variable Y, and a random sample X1, ·.. , Xn. A...

A: Expectation gives the most likely value of a random variable.

Q: Classify the following recurrent Markov chains as periodic or aperiodic. b) 4 4 3 2 3 c) d) 5 5 1 4 ...

A: " Since you have posted a question with multiple sub-parts, we will solve the first three subparts f...

Q: 7. How many ways are there that in a class of 60 students, 2 students will not have the same birth d...

A: Here Given 60 Students Now Assume that there is 365 Days in one year

Q: An unbiased die is thrown twice. Find the probability distribution of the number of sixes.

Q: If the random variable ?takes the values 1, 2, 3, 4 such that 3P(X=1)= 4P(X=2 )= P(X=3) = 5P(X=4). F...

A: It is given that, 3P(X=1)= 4P(X=2 )= P(X=3) = 5P(X=4)

Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: em 4. Players arrive at a casino at rate A, and begin betting be the total amount they lose by time ...

A: *Answer:

Q: There is a regression equation. It is Weight = - 180 + 5Height. The mean weight is 155 pounds with ...

A: Given information: Mean weight is 155 pounds with a standard deviation of 30 pounds The mean height ...

Q: lesser than the blue balls and the rest are purple balls. If a ball is to be picked at random, find ...

Q: 35. A card is drawn from a standard deck of 52 cards. What is the probability that the card drawn is...

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

Q: Calculate the posterior probability

Q: (a) E(- log X) > – log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³

A: Question:

Q: An urn contains 7 white and 3 red balls. Two balls are drawn together at random from the urn. Find t...

Q: From a city population, the probability of selecting (i) a male or a smoker is 9/10, (ii) a male smo...

Q: For the sample: 45 84 73 58 54 73 52 60 51 80. Determine the variance and round answer to 2 decimal ...

Q: A salesman is known to sell a product in 3 out of 5 attempts while another salesman in 2 out of 5 at...

Q: Which formula would you use to solve this problem? The population percentage is 46%. What is the pro...

Q: A card is drawn from an ordinary deck. Match the following with their probab 10 2 3 10 10 10 A diamo...

A: Given that - n (s) = 52

Q: (a) The mass of a small loaf of bread is normally distributed with a mean of 500g and a standard dev...

Q: A regional telephone company operates 3 identical relay stations at different locations. During a pe...

Q: Which of the following statements is correct? Select one: a. If there is less variability within the...

A: Introduction: It is required to identify each statement as true or false

Q: A random variable X is defined by Z = log X, where EZ = 0. Is EX greater than, less chan, or equal t...

Q: 1. Answer the following: Given: A = {1, 2, 3, 4, 5, 6}, B = {2, 4, 5, 6}, and C = {1, 6, 7}. B'nC'= ...

Question

a and b please thank you!

Let X be a continuous uniform random variable on [a, b]:
X ~ U[a, b].
a Write down the pdf and cdf of X.
b Calculate the expectation and the variance of X.

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the moment-generating function of the contin-uous random variable X whose probability density is given by f(x) =1 for 0 < x < 10 elsewhere and use it to find μ1,μ2, and σ2.
Let the joint pdf for the continuous random variables X and Y be: f(x,y) = { 4xy; 0<x<1, 0<y<1 0; elsewhere } What is the joint CDF of X and Y?
Let A and B be independent exponential random variables, both with mean 1. If U = A + B and V = A/B, find the joint pdf of U and V.
For any continuous random variables X, Y , Z and any constants a, b, show the following from the definition of the covariance:
Let X and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.
Let X be a random variable with pdff(x) = 4x^3 if 0 < x < 1 and zero otherwise. Use thecumulative (CDF) technique to determine the pdf of each of the following random variables: 1) Y=X^4, 2) W=e^(-x) 3) Z=1-e^(-x) 4) U=X(1-X)
Let X be a random number between 0 and 1 produced by the idealized uniform random number generator. Use the density curve for X, shown below, to find the probabilities:
Let X1 and X2 be independent chi-square random variables with r1 and r2 degrees of freedom, respectively. Let Y1=(X1/r1)/(X2/r2) and Y2=X2. (a) Find the joint pdf of Y1 and Y2.
Let a random variable X has the CDF as;Fx(x) = 1 ; x ≥ 1 1/2+x ; 0 ≤ x < 1 0 ; x < 0 Verify that Fx(x) is a CDF. Also- (i) find the PDF of X (ii) Calculate E[ex ] (iii) Determine the probability P[X = 0|X ≤ 0.5]
Let Y1 < Y2 < Y3 be the order statistics of a random sample of size 3 froma distribution having the pdf f(x) = 2x, 0 < x < 1, zero elsewhere. Show thatZ1 = Y1/Y2, Z2 = Y2/Y3, and Z3 = Y3 are mutually independent.
Let X be a random variable with pdf given by fX(x) = 1/[π(1 + x2)] for all real number x. Prove that X and 1/X are identically distributed by showing that they have the same probability distribution.
Suppose that X, Y , and Z are random variables with a joint density f(x, y, z) = ( 6/((1+x+y+z)^4)) , when x, y, z > 0, and 0, otherwise. Determine the distribution of X + Y + Z.