2. [Transformations] Consider X ~ U(0, 1) with the probability mass function1, x = (0,1)fx(x) =0, otherwise(a) Find support and PDF for Y = log(X).(b) Find the moment generating function (MGF) of Y.(c) Using MGF, find the first two moments of Y.

Part (a):To find the support and probability density function (PDF) for Y=log(X), we need to first…

Answered: 2. [Transformations] Consider X ~ U(0,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Example 23: Let f(x, y) = xe* (y + 1) ; x > 0, y > 0 %3D = 0, elsewhere. Find moment generating function of XY.
Logistic regression aims to train the parameters from the training set D = g(0¹ x) {(x(i),y(¹)), i = 1, 2,...,m, y € {0, 1}} so that the hypothesis function h(x) 1 (here g(z) is the logistic or sigmod function g(z) 1+ e-z new instance x being labeled as 1. Please derive the following stochastic gradient ascent update rule for a logistic regression problem. 0₁ = 0₁ + α(y(¹) - h₂(x)))x) = ) can predict the probability of a
(vi) Given below is a joint pdf of X₁ and X2₂ which are independent exponential random variables with parameter X. f(x1, x2) Find the joint probability density function (pdf) of Y₁ = X₁ − X₂ and Y₂ = X₁ + X₂ using the transformation method. =e-21-x2 0 < x1 <∞0,0 < x₂ <∞
QUESTION 3 A wholesaler must decide how many computers to purchase before they know how many they will be able to sell to local retailers. The wholesaler purchases the computers for S300 each and sells them to retailers for $350 each. If the wholesaler is not able to sell them to a retailer then the wholesaler can return them to the manufacturer (for a refund of the S300 cost), but the wholesaler must pay $40 per computer that it returns to the manufacturer (in shipping, handling, and insurance costs). The following probability distribution describes the number of computers the wholesaler may possibly sell to local retailers: there is a 21% chance that they will sell 900 computers, a 56% chance that they will sell 1200 computers; otherwise, they will sell 1500 computers. What is the expected number of computers the wholesaler will sell? (please round your answer to 1 decimal place)
7. Suppose that the random variable X have the pdf f (x) = e-a*/2, x > 0 and 0 otherwise. 2T (a) Find E(X) and Var(X). (b) Find the transformation g(X)= Y and values of a and B such that Y ~ I(a, B).
Finding the orthogonal trajectories of y? = x² (1 – cx)
Let X and X, independence r.v. have same moment generating function (-) where tsa, let Y=aX+bX, , then My (1) is 1
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O Messenger O Set-15.pdf Sy y=(-2x)/(5x-2); fine (dy)/(dx) - Ste x b Calculus Question | bartleby M Inbox (455) - nmajumder202130 X + O File | C:/Users/DELL/Downloads/Set-15.pdf Set-15.pdf 1 / 1 152% 1. Determine whether f(x) = |x+ 1| is continuous at x = -1. dy 2. Find the differentiation () using definition with limit of the following: 1 -2x Y = 5x 2 dy of the function y(x) = d.x -1 3. Find tan (2x) 2+x² 4. Let f(x) = 5+12x – x³. Find (a) the open intervals on which f is concave up, (b) the open intervals on which ƒ is concave down and (c) the x-coordinates of all inflection points. 5. Find the Maclaurin series of the function f(x) = . ENG 9:25 AM 0 Type here to search 80°F Rain showers INTL 7/30/2021 (1 ... ... 立 II
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2. [Transformations] Consider X ~ U(0, 1) with the probability mass function 1, x = (0,1) fx(x) = 0, otherwise (a) Find support and PDF for Y = log(X). (b) Find the moment generating function (MGF) of Y. (c) Using MGF, find the first two moments of Y.