Question: Show that H(X) log|X | for any distribution pX . Conclude that for random variables taking values in [n] := {1, . . . ,

Show that H(X) log|X | for any distribution pX . Conclude that for random variables taking values in [n] := {1, . . . , n}, the distribution which maximizes H(X) is Uniform([n]). Hint: log is a convex function

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 Mathematics Questions!

Write the meaning of each of the following terms without referring to the book (or your notes), and compare your definition with the version in the text for each: a. constant or intercept b....

Plz answer ASAP The derivative of a cubic function is a O quartic function 0 cubic function O linear function O quadratic function

Please answer all the required questions in detail I hope the answer is not copy-paste I hope that the answer will be according to the concepts in the chapter 3 The following article summarizes the...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

i just need to solve part 1 please Part 1 Consider a network that has four nodes n1, n2, n3 and n4, and six directed arcs of the form a1 = (n1, n2), a2 = (n1, n3), a3 = (n2, n3 ), a4 = (n3), n2), a5...

13. (3 points) Consider a scalar-valued random variable X that takes values {1,2,3,4} with probabilities Px(1) = 0.2, px (2) = 0.3, px(3) = 0.25, and px (4) = 0.25. Compute the mean and variance of...

In the picture Assessment DIRECTION: Write your answer on a separate sheet of paper. A. Multiple Choice. Choose the letter of the best answer. 1. If three coins are tossed, which is NOT a possible...

1. Let &, k > 0, be independent random variables taking only the integers. Let S = {0, +1, 12, ..., IN}, where N = co is allowed. Let Xo be another random variable, independent of the sequence ,...

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...

Quisha started her business, Q-Anchovies in January 2019, earning $21,000 in revenues and a profit of $1,000. In 2020, she grew her revenues to $33,000 and generated a profit of $10,500. For 2021,...

Let X and Y be random variables with values in {1, 2, 3, 4, 5, 6} with distribution functions PX and PY given by PX (j) = a j, PY (j) = b j . (a) Find the ordinary generating functions hX (z) and hY...

A newly developed compound is being considered for use as the working fluid in a small Rankine-cycle power plant driven by a supply of waste heat. Assume the cycle is ideal, with saturated vapor at...

Suppose your uncle is 40 and has a plan to retire at age 70, but his fortune teller told him that he will live for fifty more years. If he would like to have a steady income of $150,000 per year...

Find the first derivative of each of the following functions: ( a ) f ( x ) = Z 1 x 3 cost dt [ 5 ] ( b ) h ( x ) = Z x x v 2 + 2 dv [ 5 ] ( c ) g ( x ) = Z 1 1 3 x u 3 1 + u 2 du [ 5 ] Q

A political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of 1000 registered voters, 482 favor...

Write a VBA function for f(x) = x 2 ? 3. A 1 Exercise 1 2 3 Ix -2

What information is recorded on the statement of shareholders equity?

For each system shown in Figure P3.9, write the state equations and the output equation for the phase-variable representation. R(s) 8s + 10 C(s) s4 + 5s + s2 + 5s + 13 (a) R(s) C(s) s4+ 2s3+ 12s2+ 7s...

A furniture making business manufactures quality furniture to customers? orders. It has three production departments and two service departments. Budgeted overhead costs for the coming year are as...

Determine if the overhead allocated to the product relates to a single plantwide overhead rate method, multiple production department factory overhead rate method, or activity-based costing...

IRS. In a random survey of 226 self-employed individuals, 20 reported having had their tax returns audited by the IRS in the past year. Estimate the proportion of self-employed individuals nationwide...

Awareness survey. A telemarketer at a credit card company is instructed to ask the next 18 customers that call into the 800 number whether they are aware of the new Platinum card that the company is...

National health insurance. An investigator at one of Japans 47 prefectures wants to know how many citizens are in the National Health Insurance system (Kokumin- Kenk-Hoken) or in the Employees Health...