![Problem 3: Assume the continuous random variable X follows the uniform[0,1] distribution, and define another random variable Y- In () 1-X a) Determine the CDF of Y. Hint: start by writing P(Y y), then show that P(Y y) = P(X s g(v)), where g(y) is a function that you need to determine. b) Determine the PDF of Y.](http://img.homeworklib.com/questions/cb41d6d0-78c2-11ea-82f0-11e1e06f7e45.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
Problem 3: Assume the continuous random variable X follows the uniform[0,1] distribution, and define another random...
Assume the continuous random variable X follows the uniform [0,1] distribution, and define another random variable...
Assume the continuous random variable X follows the uniform
[0,1] distribution, and define another random variable
We were unable to transcribe this imagea) Determine the CDF of Y. Hint: start by writing P(Y ), then show that P(Y y) = P(X s g(v)), where g(y) is a function that you need to determine. b) Determine the PDF of Y.
Suppose that U is a random variable with a uniform distribution on (0,1). Now suppose that...
Suppose that U is a random variable with a uniform distribution on (0,1). Now suppose that f is the PDF of some continuous random variable of interest, that F is the corresponding CDF, and assume that F is invertible (so that the function F-1 exists and gives a unique value). Show that the random variable X = F-1(U) has PDF f(x)—that is, that X has the desired PDF. Hint: use results on transformations of random variables. This cute result allows...
STAT 115 Let X be a continuous random variable having the CDF Fx(x) = 1 -...
STAT 115 Let X be a continuous random variable having the CDF Fx(x) = 1 - e^ (-e^x) (1) Find the Probability Density Function (PDF) of Y=e^X. (2) Let B have a uniform distribution over (0,1). Find a function G(b) and G(B) has the same distribution as X.
X is a positive continuous random variable with density fX(x). Y = ln(X). Find the cumulative...
X is a positive continuous random variable with density fX(x). Y
= ln(X).
Find the cumulative distribution function (cdf) Fy(y) of Y in terms of the cdf of X. Find the probability density function (pdf) fy(y) of Y in terms of the pdf of X. For the remaining problem (problem 3 (3),(4) and (5)), suppose X is a uniform random the interval (0,5). Compute the cdf and pdf of X. Compute the expectation and variance of X. What is Fy(y)?...
Between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
Between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
Let the random variable X have a uniform distribution on [0,1] and the random variable Y...
Let the random variable X have a uniform distribution on [0,1] and the random variable Y (independent of X) have a uniform distribution on [0,2]. Find P[XY<1].
5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a)...
5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a) Find P(X> 3). (b) Instead of following a uniform distribution, suppose that X assumes values in the interval [0, 8) according to the probability density function pictured to the right. What is h the value of h? Find P(x > 3). HINT: The area of a triangle is base x height. 2 0 0
Problem # 8. a) Let X be a continuous random variable with known CDF FX(x). LetY = g(X) where g(·) is the so-called sign...
Problem # 8. a) Let X be a continuous random variable with known CDF FX(x). LetY = g(X) where g(·) is the so-called signum function, which extracts the sign of its argument. In other words, g(X) = { -1 x<0, 0 x=0, 1 x>0 } Express the PDF fY (y) in terms of the known CDF FX(x). b) Let X be a random variable with PDF: fX(x) = { x/2 0 <= x < 2, 0 otherwise} Let Y be...
STAT 120 Let X be a continuous random variable having the CDF Fx(x) = 1 -...
STAT 120 Let X be a continuous random variable having the CDF Fx(x) = 1 - e^ (-e^x) Let B have a uniform distribution over (0,1). Find a function G(b) and G(B) has the same distribution as X.
Assume the continuous random variable X follows the uniform
[0,1] distribution, and define another random variable
We were unable to transcribe this imagea) Determine the CDF of Y. Hint: start by writing P(Y ), then show that P(Y y) = P(X s g(v)), where g(y) is a function that you need to determine. b) Determine the PDF of Y.
Suppose that U is a random variable with a uniform distribution on (0,1). Now suppose that f is the PDF of some continuous random variable of interest, that F is the corresponding CDF, and assume that F is invertible (so that the function F-1 exists and gives a unique value). Show that the random variable X = F-1(U) has PDF f(x)—that is, that X has the desired PDF. Hint: use results on transformations of random variables. This cute result allows...
X is a positive continuous random variable with density fX(x). Y
= ln(X).
Find the cumulative distribution function (cdf) Fy(y) of Y in terms of the cdf of X. Find the probability density function (pdf) fy(y) of Y in terms of the pdf of X. For the remaining problem (problem 3 (3),(4) and (5)), suppose X is a uniform random the interval (0,5). Compute the cdf and pdf of X. Compute the expectation and variance of X. What is Fy(y)?...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
between 0 and 4, x-UlO,4]. Another random variable, Y, is given Q1) Random variable as a function of g(x), Y X has uniform distribution g(x) where g(x)- 3-х, 2 x < 3. 0, otherwise. For parts a, b, and c, plotting the function y g(x) can be very useful. a-What is P(Y 0) [4 points] b-What is P(Y 1) 13 points] c-Derive and plot the cumulative distribution function (CDF) of Y, Frv). [10 points) d-What is probability distribution of Y,...
5. A continuous random variable X follows a uniform distribution over the interval [0, 8]. (a) Find P(X> 3). (b) Instead of following a uniform distribution, suppose that X assumes values in the interval [0, 8) according to the probability density function pictured to the right. What is h the value of h? Find P(x > 3). HINT: The area of a triangle is base x height. 2 0 0
Most questions answered within 3 hours.
-
Consider the reaction, C3 H8 + O2 --> CO2 + H2O. How many
moles of O2...
asked 1 hour ago -
You and your opponent both roll a fair die. If you both roll the
same number,...
asked 1 hour ago -
In a study of the accuracy of fast food drive-through orders,
Restaurant A had 257 accurate...
asked 1 hour ago -
Identify and describe in detail the four categories of
institutions that could be included in a...
asked 1 hour ago -
In python
class Customer:
def __init__(self, customer_id, last_name, first_name, phone_number, address):
self._customer_id = int(customer_id)
self._last_name =...
asked 1 hour ago -
What is an example of a limitation in implementing a new
ERP system and how it...
asked 1 hour ago -
In a section of 9.7cm of an artery with a radius of 2.6mm there
is a...
asked 1 hour ago -
the two carboxylic acid groups of aspartic acid have different
acidities with pKa values of 2.1...
asked 1 hour ago -
Would CuCO3 aqueous salt combined with calcium chloride
form a solid precipitate? If so, what would...
asked 1 hour ago -
How do ECM Solutions assist in embedding a culture of continuous
improvement in an organization? (Project...
asked 2 hours ago -
Directions
These directions introduce the idea of Essential Questions.
Since this may be a new concept...
asked 2 hours ago -
1.b. Fiscal policy is said to suffer from ‘crowding out’.
Explain what this means and why...
asked 2 hours ago