3. Entropy is also defined when classification is into three or more classes.The entropy of a set S relative to n distinct classes is defined as:22Entropy (S) = [- -Pi log₂ Piwhere p; is the proportion of the Set S in class I, with i=1, ..., n. Notice that thelogarithms are still calculated base 2.Calculate the entropy of the set S, where p₁=620JP2=920=,P3 = 2500

The entropy of the set S can be calculated by inserting the probabilities of the events p1,p2 and p3…

Answered: 3. Entropy is also defined when…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A group of students on a Mathematics for Economics course were surveyed to see how long they spent dreaming about algebra each night. The grouped frequency table is given below. a) interval cumulative time spent dreaming frequency f mid point f x x frequency less than 10 minutes more than 10 and at 12 most 20 minutes more than 20 and at 15 most 35 minutes more than 35 and at 3 most 80 minutes Efæ = Ef =
A mixture of sucrose and water was heated on a hot plate, and the temperature (in °C) was recorded each minute for 20 minutes by three thermocouples. The results are shown in the following table. Time 0 1 2 3 4 5 6 7 8 SPIEBALGAKOO | | 9 10 11 12 13 14 15 16 17 18 19 20 FO T1 20 18 29 32 37 36 46 46 56 58 64 72 79 84 82 87 98 103 107 103 102 H T2 18 22 22 25 37 46 45 44 54 64 69 65 80 74 87 93 90 100 100 103 103 T3 21 11 26 35 33 35 44 43 63 68 62 65 80 75 78 88 91 103 112 107 104 Someone else suggests averaging the three temperature measurements at each time to obtain T = (71+ 72 + 73)/3. Compute the 12 ‒‒‒ Next >
2
Let 6=1t Let H= subgraupof Ğ G or not
The number of years N(r) since two independently evolving languages split off from a common ancestral language is approximated by N(r) = – 4000 lIn r where r is the proportion of the words from the ancestral language that are common to both languages now. a. N(0.9) = (Round to the nearest tens place.) %3D b. N(0.4) = (Round to the nearest hundreds place.) c. N(0.1) = (Round to the nearest thousands place.) d. How many years have elapsed since the split if 60% of the words of the ancestral language are common to both languages today? years have elapsed since the split. (Round to the nearest hundreds place.) e. If two languages split off from a common ancestral language about 2000 years ago, find r. r = (Round to the nearest tenth as needed.)
Find the integral monthly average price of each item (sugar, Flour, Eggs, Cooking Oil) given in the table. Then draw the Bar- Graph, Pictogram and Pie Chart of the obtained data (Items Vs monthly average prices).
In each case, determine whether or not the lines have a single point of intersection. If they do, give an equation of a plane containing them. a) r₁ = (5t, 2t - 1,2t - 2) and r₂ = b) r₁ = (3t, -4t + 1,t— 5) and r₂ = (2t — 2, –t, −t − 1) (Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if lines do not intersect.) (a) the equation of the plane: (t-6, -t + 5,t - 8) (b) the equation of the plane:
b. The following are the time (in months) to relapse for patients who had acute leukemia when being treated with a particular drug: 10, 7,32', 23, 22, 6, 16, 34", 32", 25", 11", 20", 19", 6, 17", 35", 6, 13, 9", 6", 10" Obtain the Kaplan-Meier estimate of the survivor function.
9. The mean value of a function f(x) from a to b is given by
6
For numbers 18 to 21: A study was conducted using 50 undergraduates at a large private university who volunteered to participate in the research as partial fulfillment of a course requirement. One of the items studi ed was the maximum daly amount of alcohol consumed in the last month. Base on the datain the following table, are there differen ces between males and females in the maximum amount of alcohol consumedin any one day in the pastmonth? Use 5% level of significance. Assume equal variances. Male 8.2 female 5.6 5.7 30 Alcohol consumed Mean Standard deviation Number of students 5.9 20 18. Which of thefollowing is the appropriate altemative hypothesis? A There are more female participants than males B. The amount of alcohol consumed by males is higherthan the amount consumed by the females. C The amount of alcohol consumed by males and females in the past month is not the same. D. The amount of alcohol consumed by males and females in the past month is the same. 19. The pooled…
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