Let X have a uniform distribution on the interval [A, B]. (a) Please write down the probability density function (pdf) (b) Please write down the cumulative density function (cdf) of X. (c) Compute the 90th percentile. (d) Compute E(X) and V(X).

Let X have a uniform distribution on the interval [A, B]. (a) Please write down the probability density function (pdf) (b) Please write down the cumulative density function (cdf) of X. (c) Compute the 90th percentile. (d) Compute E(X) and V(X).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

See similar textbooks

Related questions

Q: A random variable X has probability density function (x² + 2x + 4) for 0 < x < 3 f(x) = otherwise.…

Q: A transmission repair firm that wants to offer a lifetime warranty on its repairs has determined…

A: probability that it will last 5 or less months

Q: A random variable X has the probability density function f(x) = e* on it support [0,z]. What is its…

Q: Given the probability density function f(x) = 1 over the interval [4, 8], find the expected value,…

Q: After years of testing, Duracell has developed the probability density function p(x) = 0.08e 008x…

Q: Sketch the graph of the probability density function over the indicated interval and find the…

A: We use a graphing calculator to sketch f(x)=x/50 over [0,10]

Q: The graph to the right is the uniform probability density function for a friend who is x minutes…

Q: f (y) = a (b– y), 0 < y < b, and 0 elsewhere. If the mean of the distribution is .2, find the values…

A: The density function of Y is given by, f(y) = a (b-y) , 0<y<b Hence, ∫0ba(b-y) dy = 1…

Q: The shelf life, in days, for bottles of a certain prescribed medicine is a random variable having…

A: Probability density function of X isf(x)=5000(x+50)3 , x>0

Q: Consider a random variable X which takes on values 1 and 2 with probability 0.25 and 0.75,…

A: The provided information is:x12Pr[x]0.250.75

Q: A distribution that has been used to model tolerance levels in bioassays is the logistic…

Q: (d) Let X P(X < 1.4)? 25 25 X;. How would you use the central limit theorem to approximate

A: We want to find the probability by using central limit theorem.

Q: c) Compute the expectation of X, i.e. E(X), and the variance of X, i.e. Var(X). d) Compute the…

A: The probability density function which is also known as pdf is used to represent the density of a…

Q: The probability density function of a continuous random variable is given by y=2x−4 from x=2 to x=3.…

A: Given that, the probability density function of a continuous random variable is given by y=2x−4 from…

Q: Let the density function of a random variable X be f(x) = xe¬* for x > 0. Find a. The moment…

A: Solution:-

Q: Let X1 ~ Exp(1) and X2 ~ Exp(^2) be independent exponential random variables. (a) When A1 2,…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: A continuous random variable X has a normal distribution with mean 6. The probability that X takes a…

A: Given information Mean (µ) = 6 P(X > 15) = 0.38 P(Z > z) = 0.38 P(Z < z) = 1 – P(Z>Z) =…

Q: Hanny

A: a) PDF of Xf(x)=6xe−3x2,x≥0b)mean =0.5118median=0.4807mode=0.4082Explanation:

Q: Calculate P(2.7<x<3)

A: Solution-: The probability density function is, f(x)=16x ; 2<x<4 We want to find…

Q: Sketch the graph of the probability density function over the indicated interval. F(x) = 1/20, [0,…

Q: A random variable X has the cumulative distribution function probability density function F(x) = e*…

A: Given that, a random variable X has cdf:- F(x) = ex , [0, z ]

Q: Given the probability density function f(x)=14f(x)=14 over the interval [2,6][2,6], find the…

A: Given information: fx=14, 2<X<6, this is the density function of uniform distribution with a=2…

Q: The pH water samples from a specific lake is a random variable X with probability density function.…

Q: A tour is scheduled to start at 5:00 p.m., 5:30 p.m., and 6:00 p.m. Once the tour starts, the gate…

A: a = 4:30 pm b= 6:00 pm Now re define the random variable, x : Time elapsed after 4.30pm till the…

Q: b) Find the marginal probability density function of X, fy(x).

Q: A random variable has density function f(x)= = 1.6 1.2x, for 0 ≤ x ≤ 1. a) Calculate the variance of…

A: given function is f(x)=1.6−1.2x for

Q: Given the probability density function f(x)=15f(x)=15 over the interval [3,8][3,8], find the…

A: Given, f(x) = 1/5 where x ∈ 38 f(x) is a p.d.f of x follows uniform distribution x ~ U[ 3 , 8 ]

Q: Given the probability density function f(x)=13f(x)=13 over the interval [4,7][4,7], find the…

Q: Given the probability density function f(x)=14f(x)=14 over the interval [3,7][3,7], find the…

Q: (a) Let X defines the length in meter. The probability density function of X is f(x) = x + 1 where a…

Q: The(probability density function of a random variable, x is (x) = -(4 – x²) for 0< x < 2 4 = 0 %3D…

A: Introduction :

Q: The random variable X has a uniform density function over the interval [-1, 1]. a. Sketch the…

Q: eight where the probability density function for the weight of passenger luggage is increa al Rule…

Q: Exercise 8: (Hard) Let us suppose that f is a probability density function, and f(x) = 0 if x b.…

A: Formula for Variance:

Q: Given the probability density function f(x) = - 1 over the interval [2, 5], find the expected value,…

Question

Let X have a uniform distribution on the interval [A, B].
(a) Please write down the probability density function (pdf)
(b) Please write down the cumulative density function (cdf) of X.
(c) Compute the 90th percentile.
(d) Compute E(X) and V(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

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions

Figure I shows the piecewise function (I), (II), (III) and (IV) for cumulative distribution function F(x) for continuous random variable. F(x) (6. 1) IV III II (4.0.8333) (0.0.1667) Figure I Construct the probability density function fix). Should one of the piecewise functions (IV) is not constant, explain the changes.
Battery life between charges for the Motorolla Droid Razr Maxx is 20 hours when the primary use is talk time. The battery life drops to 7 hours when the phone is primarily used for Internel applications over cellular. Assume that the battery life in both cases follows an exponential distribution. a. Show the probability density function for battery life for the Droid Razr Maxx phone when its primary use is talk time. b. What is the probability that the battery charge for a randomly selected Droid Razr maxx phone will last no more than 15 hours when its primary use is talk time? c. What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last more than 20 hours when its primary use is talk time? d. What is the probability that the battery charge for a randomly selected Droid Razr Maxx phone will last no more than 5 hours when its primary use is Internet Applications?
A probability density function of a random variable is given by f(x)=x/8-1/2. on the interval [4,8] Find the median of the random variable, and find the probability that the random variable is between the expected value (mean) and the median.
The function f(x) is the probability density function, that describes the random variable travel time X. f(x) = {xe®, x>0 0, X ≤0 a.) What is the probability that the travel time is less than 2.5 hours? b.) What is the probability that the travel time is between 1 to 2.5 hours? c.) Find the mean and variance of the given probability density function
The random variable X models the loss in thousands of dollars due to a fire in a commercial building. Its density function is f(x) = 0.005*(20-x) for 0 being less than or equal to x and x being less than or equal to 20 and f(x)= 0 otherwise. Given that a loss due to the fire exceeds $8000, find the probability the loss exceeds $16000.
The relationship between probability distribution function F(x) and the probability density function d f(x) is f(x) = -F(x) dx Select one: True False
The function f(x) is the probability density function, that describes the random variable travel time X. f(x) = {xe3,_x>0 0, X ≤ 0 a.) What is the probability that the travel time is less than 2.5 hours? b.) What is the probability that the travel time is between 1 to 2.5 hours?
The random variable X has probability density function 3, 1< a < 2 f(x) = otherwise. Calculate Var(4X +7).
Let X be a random variable with the probability density function. f(r) = 2c for x = 1,2,3, 4, ..., 0 for some constant c. What is the value of c What is the probability that X is even?
Let X and Y have the joint probability density functionf(x, y) = 5, for 0 < x < y < 1.(i) Find the marginal probability density function of X and Y.(ii) Find the conditional probability density function of X, given Y = y.(iii) Find the conditional mean of X, given Y = y.(iv) Find the conditional variance of X, given Y = y.
Let X and Y random variables have independent Gamma distributions with X-Gamma(1, 6) and Y-Gamma(2, B). a. Find the joint probability density of Z, = X + Y, Z, = X+Y a. Find the marginal pdf of Z2.
let X denotes the percentage of time out of a 40-hour workweek that a call center agent is directly serving a client by answering phone calls. Suppose that X has a probability density function defined by f(x) =3x² for 0 ≤ x ≤ 1. Find the mean and variance of X. Interpret the results.