For a particular examination, there are four subjects to study. The ordered pair (e i , w i ) denotes that for i-th subject, a student has to put in a total of e i hours of study to score a maximum of w i marks. Suppose there are only 30 hours to prepare for the exam. (e i , w i ) pairs are given for four subjects S 1 , S 2 , S 3 , S 4 respectively as (11,10), (12, 15), (24,20), (25,25). There are two kinds of people- A and B. A cannot understand any subject by studying it partially and B gets marks in proportion to the effort she puts in to- wards any subject. For both A and B, find out the maximum marks that each of them can obtain. Show the solution obtained by each of the following greedy strategies for choosing the subjects to study for A: a) Maximum marks per unit effort b) Maximum marks subject first c) Least effort subject first
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
For a particular examination, there are four subjects to study. The ordered pair (e i , w i ) denotes that for i-th subject, a student has to put in a total of e i hours of study to score a maximum of w i marks. Suppose there are only 30 hours to prepare for the exam. (e i , w i ) pairs are given for four subjects S 1 , S 2 , S 3 , S 4 respectively as (11,10), (12, 15), (24,20), (25,25). There are two kinds of people- A and B. A cannot understand any subject by studying it partially and B gets marks in proportion to the effort she puts in to- wards any subject. For both A and B, find out the maximum marks that each of them can obtain. Show the solution obtained by each of the following greedy strategies for choosing the subjects to study for A:
a) Maximum marks per unit effort
b) Maximum marks subject first
c) Least effort subject first
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