Question: 1.32 () Consider a vector x of continuous variables with distribution p(x) and corresponding entropy H[x]. Suppose that we make a nonsingular linear transformation of

1.32 () Consider a vector x of continuous variables with distribution p(x) and corresponding entropy H[x]. Suppose that we make a nonsingular linear transformation of x to obtain a new variable y = Ax. Show that the corresponding entropy is given by H[y] = H[x] + ln|A| where |A| denotes the determinant of A.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Pattern Recognition And Machine Learning Questions!

Budgeting for Nonprofit Organizations Although budgeting is just as important for nonprofit organizations as for for-profit companies, the approach taken toward budgeting can be very different. In...

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

A network based service manages persistent objects. The service must enforce an access control policy to protect the objects. (a) Discuss how this access control might best be implemented for the...

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

1. 2. 3. What is a stack data structure and what is a queue data structure? Compare the similarities and differences of stack and queue data structures. What are the operations in stack and queue...

In Figure a string, tied to a sinusoidal oscillator at P and running over a support at Q, is stretched by a block of mass m. The separation L between P and Q is 1.20 m, and the frequency f of the...

"2 (14 pts) Based upon your financial forecast for the years 20X3 - 20X7, compute 2a through 2d below FROM THE VIEWPOINT OF THE SHARK, placing your final results in the yellow highlighted area....

What is a synapse? Explain the difference between an excitatory and an inhibitory synapse.

Sante Fe Corporation's sales office and manufacturing plant are located in State A. Sante Fe also maintains a manufacturing plant and sales office in State B. For purposes of apportionment, State A...

For each of the following items considered independently, indicate whether the circumstances call for an addition modification (A), a subtraction modification (S), or no modification (N) in computing...

Perk Corporation is subject to tax only in State A. Perk generated the following income and deductions. Federal taxable income .............. $300,000 State A income tax expense ............. 15,000...

A survey by CPA Australia shows that at least one in four small businesses are affected by fraud. Employee fraud was the most common type reported. Comment on whether fraud is just part of the cost...

Miss Geraldine is 50 years old. She needs $690,000 in life insurance. Find her monthly premium for a 20 pay life plan. $2,041.83 $22,487.1. O $19,430.4 $1,764.28

Exercise 2-17A Prepare a trial balance (LO2-6) Below is the complete list of accounts of Sooner Company and the related balance at the end of April. All accounts have their normal debit or credit...