Answered: Suppose that X ~ Unif[0, 1] and let Y =…

Suppose that X ~ Unif[0, 1] and let Y = e^X. (a) Find the cumulative distribution function of Y .(b) Find the probability density function of Y .

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.1: Continuous Probability Models

Problem 28E

See similar textbooks

Related questions

Q: The probability density function of the time to failure of an electronic component in a copier (in…

A: The time to failure of an electronic component in copier follows Exponential Distribution with pdf…

Q: Consider two independent random variables, X and Y, which are both exponentially distributed with…

A: Given X and Y are independent X, Y~exp(λ) Result: If x and y are independent then E(XY)=E(X)E(Y)

Q: If (X,Y) has an uniform on the bounded region G: x²+²<2. Give the probability density function of…

Q: therwiSe Is this a proper density function of a continuous random variable?

Q: A stock solution of hydrochloric acid (HCl) supplied by a certain vendor contains small amounts of…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: A continuous random variable X that can assume values between x = 0 and x = 4 has a density function…

Q: A continuous random variable has a density function f (X)=2(5-x)/5 , where 2 2.2) P (2.1 ≤ ? ≤ 2.7)

A: Given density function is, f(x)=2(5−x)5, 2<x<3

Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A: The probability density function of X is obtained below: f(x)=0.5e-0.5x;x≥0 where x is a random…

Q: The random variables X and Y are related as Y= X. Find the density function of voriable Y.

Q: For the continuous random variable with probability density function: sin(x), 0≤x≤ f(x) =< 2 0,…

A: For finding median through probability density function we use: ∫0Mf(x).dx = 12 M: Median value

Q: The probability density function of a random variable X is given by 0<x<1 f (x) = {2-x l<x<2…

A: I have shown all the steps Area below lower bond is 0.125 using Chebyshev's theorem

Q: Suppose that the lifetime X (in hours) of a certain type of flashlight battery is a random variable…

Q: be a random sample of size n and given a >( >0 with the probability density function of X is…

Q: Let sinx 0 <x<n f(x) = otherwise be probability density function of X, Compute var(x)?

A: The variance of X is defined as Var(X) = E(X2) - (E(X))2

Q: Suppose the duration (in hours) of a certain valve is a random variable X with density function f(x)…

A: Given information: fx=648x-4, x>6

Q: Please answer part c, d, and e ONLY. (Last 3 parts)

Q: A continuous random variableX that has a density function given by for 1<r < 4 | f(x) = elsewhere…

A: We have given that Probability density function f(x)= 1/5 ,- 1 <x< 4

Q: A continous random variable has density function f(x)=(3x2)/(03) for Osxse, for some 0>0, and zero…

A: First we have to determine mode and median of given distribution.

Q: The moment generating function of the random variable X having the probability density function f(x)…

A: Given a probability density function of x, we need to find moment generating function of X

Q: function fx,y given by Suppose that X and Y have a joint probability density -{..-* fxy(x, y) =…

A: Given f(x,y)=ce-2(x+y) x>0, y>0

Q: The probability density function of the gamma distribution is as follows. f (x) = Г(а) ßx , x>0, a,…

Q: A random variable Y has probability density function given by fly)= 2y for 0 1)

A: We have to calculate the P(Y > 1) for the given probability density function of Y.

Q: The life (in years) of a laptop battery has a probability density function defined by P(x) -z /5 5…

Q: For a continuous random variable x, the height of the function at x is the probability at a given…

A: For a continuous random variable x, The height of the function at x is given by,

Q: Suppose that X and Y are jointly distributed with joint probability density function defined on the…

A: Since X and Y are jointly distributed we can say that there exists a probability distribution…

Q: Let X and Y be continuous random variables with joint probability density function given by 4.…

A: To find the covariance of X and Y we need to find the marginal distribution of X and Y first.

Q: Suppose paint in millimeters at a randomly chosen point on a randomly chosen car panel, and that X…

A: Given Suppose that the random variable X measures the thickness of the paint in millimeters at a…

Q: 2. X1,...,X, are iid exponential(1) random variables, with density function f(x) = e~*, c.d.f. F(r)…

Q: A random variable X has the probability density function (pdf) shown in he figure below. fx (2)

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…

Q: Consider a continuous random variable X with probability density function given by f(x) = { 0" Į kx…

A: Given probability density function,f(x) =k(x) for 1≤x≤50 otherwise

Q: A continuous random variable has a density function f(x)= 2(5-x)/5 , where 2<x<3. Calculate the…

A: Graph:

Q: Let X and Y be continuous random variables with joint density function for 0 SIS1, x Sys2x f6, y) =…

A: Let X and Y be continuous random variables with joint density function fx,y=83xy for 0≤x≤1 ,…

Q: A continuous random variable has a probability density function of f(x) = 2x² for 0 < x≤ 2 and is…

A: Given that A continuous random variable has a probability density function of f_{x}(x) = 2x2 for 0…

Q: If X and Y are two random variable with the joint probability density function give by : f(x, y) = {…

Q: Suppose that X and Y have a joint probability density function given by fxx(1, y) = if 1, y 2 0…

A: A joint probability density function gives the probability for two random variables. For example two…

Q: A random variable X has probability density function for 0 < x < 2, 4 f(x) = { +(2x –- 3) for 2 < x…

A: Given:

Q: Determine the mean value of the continuous exponentially distributed random variable - (х-а) b X>a…

Q: A random variable X has probability density function given by for 1 < x < 3 f(x) = otherwise.…

A: Given probability density function ,fx=14x for 1≤x≤30 otherwise

Q: Suppose lifetime of a particular type of old mobile, X, can be modelled by the probability density…

A: Given, f(x) = 0.5e-0.5x : x≥0 where x is a random variable follows exponential distribution with…

Q: Suppose X is exponentially distributed with mean 2. Let Y = eX. What is the density function of Y?

A: Answer:- Given that, X is exponentially distributed with mean 2.

Q: Then the probability density of Y = In (X) is equal %3D

A: The CDF Y is given by

Q: then what is the marginal density function of X, where nonzero?

Q: Find the density function of the random variable X if the characteristic function is Ør (@)…

Q: Suppose the lifetime (in years), Y, of a mechanical component is an exponential random variable with…

A: Exponential Distribution: A continuous random variable X is said to follow Exponential distribution…

Q: A machine has a useful life of 4 to 9 years, and its life (in years) has a probability density…

A: given pdf function fx=115+13xand x= machine has usefull life ; 4 ≤x≤7

Q: f(x) = kx³/² 0 ≤ x ≤ 5 and 0 otherwise.

A: Solution

Question

Suppose that X ~ Unif[0, 1] and let Y = e^X.

(a) Find the cumulative distribution function of Y .
(b) Find the probability density function of Y .

Video Video

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

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 4 images

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, probability and related others by exploring similar questions and additional content below.

Similar questions

10) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.
Suppose X~Uniform(0,1), and Y = -ln (1-x). (a). Find the probability density function of Y (b). The name of the distribution of Y.
Find k such that the function is a probability density function over the given interval. Then write the probability density function. f(x)=kx^2, [-4,2] k= f(x)=
The probability density function of a known distribution is 1 f(ul0) = T ()exp (-), y>0, r(v) where I(v) is the Gamma function, and 0, v > 0. (a) Show that this distribution falls within the exponential family given v is known. Specify the components: a(y), b(0), c(0), d(y). (b) Find the mean and variance of this distribution using the expressions obtained in part (a). Results should be given in terms of 0 and v. (c) Point out one practical issue with model fitting when the canonical link function is used.
The exponential probability density function is f(y, 2) = 2e-y for y, 220 Show that the exponential distribution is a member of the exponential family.
Let X be a continuous random variable with probability density function f(x) = 2(1-x), 0<=x <= 1. If Y = 2X - 1, find the probability density function of Y. x is lower case X is upper case. I need to get upper case of Y
Show that f(x)f(x) is a probability density function, Find E(X)E(X) and Var(X)Var(X).
Suppose that the probability density function of the length of computer cables is f (x) = 2x/(32) for x between 0 and 3 meters. Determine the mean of the cable length. Please enter the answer to 2 decimal places.
The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is the life length of transistor 1 and Y is the life length of transistor 2. The joint probability density function of (X; Y ) is given by ´2e-(x+2) x 2 0, y 20 fx,y(x,y)=| else Then the probability that the first transistor burned during half hour given that the second one lasts at least half hour equals Select one: a. 0.3935 b. 0.606 c. 0.7772 d. 0.3669 e. 0.6318
Suppose that the continuous random variable X has CDF Fx(X) = {(x-2)/x , x>2 and 0, x=<2} a. Determine, and sketch, the pdf (probability density function) of X. b. Find the mean and variance of X c. Determine the pdf of the random variable Y=X^2
A stick of length 8 meters is randomly broken into two parts. Find the cumulative distribution function (cdf) and the probability density function (pdf) of the length of the shorter part. Cumulative distribution function: F(x) = { Probability density function.: f(x) = { I I if 04. otherwise. if if if
Q2/ If the probability density function of X is : f(x)% = (1+e-*)2 1 then what is the probability density function of y= %3D 1+e-*