Prove that if can take on any of possible values with respective probabilities P 1 , ...,
Question:
Prove that if can take on any of possible values with respective probabilities P1, ..., Pn, then H(X) is maximized when Pi = 1/n, i = 1, ... , n. What is H(X) equal to in this case?
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (8 reviews)
The entropy of a discrete random variable X with possible outcomes x1 x2 xn and respective probabili...View the full answer
Answered By
BillClinton Muguai
I have been a tutor for the past 5 years. I have experience working with students in a variety of subject areas, including computer science, math, science, English, and history. I have also worked with students of all ages, from elementary school to college. In addition to my tutoring experience, I have a degree in education from a top university. This has given me a strong foundation in child development and learning theories, which I use to inform my tutoring practices.
I am patient and adaptable, and I work to create a positive and supportive learning environment for my students. I believe that all students have the ability to succeed, and it is my job to help them find and develop their strengths. I am confident in my ability to tutor students and help them achieve their academic goals.
0.00
0 Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
A random variable can take on any of possible values x 1 , ... , x n with respective probabilities p(x i ), i = 1, ..., n. We shall attempt to determine the value of by asking a series of questions,...
-
Prove that if h > 1, then 1 + nh (1 + h)n for all nonnegative integers n. This is called Bernoulli's inequality.
-
Prove that if z = x + I iy, then |ez| = ex, phez = y.
-
Your client has offered a 5-year, $1,000 par value bond with a 10 percent coupon. Interest on this bond is paid quarterly. 1) If your client is to earn a nominal rate of return of 12 percent,...
-
Balance these redox reactions by the half reaction method. a. Ca + H+ ( Ca2+ + H2 b. Sn2+ ( Sn + Sn4+ (Hint: both half reactions will start with the same reactant.)
-
Start-Up Industries is a new firm that has raised $200 million by selling shares of stock. Management plans to earn a 24% rate of return on equity, which is more than the 15% rate of return available...
-
Which type of magnetic pole is located near Earth's geographic South Pole?
-
The Pelnor Corporation is the nation's largest manufacturer of industrial-size washing machines. A main ingredient in the production process is 8- by 10-foot sheets of stainless steel. The steel is...
-
16. Let a1, a2, 17. a <0 is: (a) 22 be in H.P. with a = 5 and a20 = 25. The least positive integer n for which " (b) 23 Sum of the series rlog. r=1 (c) 24 (d) 25 r+1 + is: r
-
This exercise is a continuation of E5-13. Proud Corporation acquired 80 percent of Stergis Companys voting stock on January 1, 20X3, at underlying book value. The fair value of the noncontrolling...
-
A pair of fair dice is rolled. Let and let equal the value of the first die. Compute (a) H(Y), (b) H Y (X). and (c) H(X, Y). (1 if the sum of the dice is 6 X = 0 otherwise
-
Determine the entropy of the sum that is obtained when a pair of fair dice is rolled.
-
The Bassos contracted with Dierberg to purchase her property for $1,310,000. One term of the contract stated, "the sale under this contract shall be closed . . . at the office of Community Title...
-
Find the equation of the line that passes through the point (1,3) and is parallel to the line y = 2x + 3. Express your equation in slope-intercept form, and give the full equation as your answer. The...
-
Discuss your written literature review on a topic: evaluating the success rate of the United Southeast Asian American Program at Fresno City College Please include introduction: restate thesis Orient...
-
Politicians who express concern about the national debt or balancing the budget often rely on analogies of personal or household finances. According to Wray, Kelton, Molser, etc., these analogies...
-
please find 8-10 sources about the following topics -monetary policy -fiscal policy -supply-side policy -inflation -how inflation has been tackled in the past? -Applications in banks for monetary,...
-
Use a diagram and words to explain the social benefit of a government program to supply social housing. Assume the market for housing is efficient and the increase in supply changes the price of...
-
Hyaluronic acid, a component of connective tissue, is the fluid that lubricates the joints. It is an alternating polymer of N-acetyl- D-glucosamine and D-glucuronic acid joined by linkages. Draw a...
-
On April 29, 2015, Auk Corporation acquires 100% of the outstanding stock of Amazon Corporation (E & P of $750,000) for $1.2 million. Amazon has assets with a fair market value of $1.4 million (basis...
-
Let X1, . . . ,X20 be independent Poisson random variables with mean 1. (a) Use the Markov inequality to obtain a bound on (b) Use the central limit theorem to approximate 20 , > 15
-
Fifty numbers are rounded off to the nearest integer and then summed. If the individual roundoff errors are uniformly distributed over (.5, .5), approximate the probability that the resultant sum...
-
A die is continually rolled until the total sum of all rolls exceeds 300. Approximate the probability that at least 80 rolls are necessary.
-
Do you think the potential sale of the Stock business in the US will be enough to relieve the current pressure on Wolco's balance sheet? What value would potentially need to be achieved to provide a...
-
Ramort Company reports the following for its single product. Ramort produced and sold 20,400 units this year. Direct materials Direct labor Variable overhead Fixed overhead Variable selling and...
-
Income from operations $990,000 $935,000 Net Income $590,040 $557,700 Interest Expense $6,600 $5,500 Total Assets $4,400,000 $3,850,000 Noninterest-bearing current liabilities $319,000 $308,000 Tax...
Study smarter with the SolutionInn App