Question: n Let p1, P2, , Pn E (0,1) be a real numbers satisfying > Pk = 1. The following quantity f is called k=1

n Let p1, P2, , Pn E (0,1) be a real numbers

n Let p1, P2, , Pn E (0,1) be a real numbers satisfying > Pk = 1. The following quantity f is called k=1 entropy and express the amount of dispersion of a set of values p1, P2, , Pn. f (P1, P2, - , Pn) > Pk log Pk. k=1 Find the values p1, P2, . , Pn when the entropy is maximized.

Step by Step Solution

★★★★★

3.30 Rating (147 Votes )

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 Mathematics Questions!

Let a, b, c, d be numbers satisfying 0

Let P1 = P1(2, 1, -2) and P2 = P2(1, -2, 0). Find the coordinates of the point P: 1/4 the way from P2 to P1

Let f(x) = log x and n N. a) Find the Taylor polynomial Pn := pnf,1. b) Prove that if x [1, 2], then c) Find an n so large that Pn approximates log x on [1, 2] to three decimal places. | log x-pn...

14. Let X be uniform over (0, 1). Find E[X\X

Let X be uniform over (0, 1). Find E[X|X

1) Let a, be R* ( meaning a, b are positive real numbers). Evaluate the following integral. Show all work clearly and use proper mathematical notation. [5 pts] e ax dx Veax + 1 b

Describe, in outline, each of the implicit surface, NURBS surface, and constructive solid geometry methods for defining three-dimensional shapes. (b) Compare and contrast the three methods. (a)...

Its macro analysis Problem 1 Consider an exchange economy in which there are only two agents, Robinson and Friday, and two goods, 1 and 2. Denote with (wp, w?) e R? and (wf, w? ) e R? the initial...

The Fourier series of a signal x[n] and its coefficients X k are both periodic of the same value Nand as such can be written (a) To find the x[n], 0 ¤ n ¤ N 1, given X k , 0 ¤ k...

A Lorenz curve is given by y = L(x), where 0 x 1 represents the lowest fraction of the population of a society in terms of wealth and 0 y 1 represents the fraction of the total wealth that is...

Consider the following scenario analysis: Rate of ReturnScenarioProbabilityStocksBondsRecession0.2-5%17%Normal economy0.51811Boom0.3234 Assume a portfolio with weights of 0.60 in stocks and 0.40 in...

Question 2 (20 Marks) Weekly sales of copy paper at Cubicle Suppliers are provided in the table below. Compute a three-period moving average and a four-period moving average for weeks 5, 6, and 7....

Andrea was an up - and - coming music producer at Too Loud Productions. One night while out at the clubs, Andrea discovered a new singer , Dylan. Andrea approached Dylan after the show and gave him...

Review Chapter 15, Table 15.4, Prisoner Dilemma . Suppose the game starts with both Jesse and Frank planning to "Stay Mum" in the lower right cell. Discuss how each player would evaluate the...

Question 78 of 81. The total amount of capital gain or loss that Allison must claim on her tax return is: ($1,985) ($1,515) $1,515 O $1,985

Can someone please help me with this, the lab seems easy but I keep messing it up, if you could help I would appreciate it, please You can even make numbers as longa as it follows the lab, I just...

The Townsend Tractor Company manufactures small garden tractors on a highly automated assembly line. Its' costing system uses two cost categories, direct materials and conversion costs. Each tractor...

Cassandra Casey operates the Futuristic Antique Store. She maintains subsidiary ledgers for accounts payable and accounts receivable. She presents you with the following information for October 2019:...

(a) Prove that for all n N, 10" = (-1)" (mod 11). (b) Consider the result for mod 9 in part (b) of Exercise 18. State and prove a comparable result for mod 11.

Suppose that a random variable Z has mean E(X) = 15 and variance Var(X) = 4, but its probability distribution is unknown. Use Chebyshev's Inequality to find the value of the constant c where Pr(|X -...

When she is about to leave a restaurant counter, Mrs. Albanese sees that she has one penny, one nickel, one dime, one quarter, and one half-dollar. In how many ways can she leave some (at least one)...

The poll described in Exercise 39 also investigated the respondents' party affiliations based on what area of the state they lived in. Test an appropriate hypothesis about this table and state your...

In April 2009, Gallup published results from data collected from a large sample of adults in the 27 European Union member states. One of the questions asked was, "Which is the most practicable and...

In Exercises 24,26, and 28, we've tested a hypothesis about whether the use of statistics in NEJM medical articles has changed over time. The table shows the test's residuals. a) Show how the...