Probability density functions can be weighted so that different properties of the distribution can be enhanced or diminished. For instance, if a set of test scores is to be used in comparing the highest performers in a class, one might want to use a pdf, , in which the probability of finding a certain score, f(x), is multiplied by that score: . A mean found using the weighted pdf might be called a score-weighted mean. Find the score-weighted mean for an exam for which the probability of finding a score is given by the function . You will need to construct the weighted pdf then use it to find the mean score.
A) 66.7
B) 60.0
C) 50.0
D) 75.0

Question

Probability density functions can be weighted so that different properties of the distribution can be enhanced or diminished. For instance, if a set of test scores is to be used in comparing the highest performers in a class, one might want to use a pdf,  , in which the probability of finding a certain score, f(x), is multiplied by that score:  . A mean found using the weighted pdf might be called a score-weighted mean. Find the score-weighted mean for an exam for which the probability of finding a score  is given by the function  . You will need to construct the weighted pdf then use it to find the mean score.
A) 66.7 
B) 60.0 
C) 50.0 
D) 75.0

Quizplus · Accepted Answer

The Answer of Probability density functions can be weighted so that different properties of the distribution can be enhanced or diminished. For instance, if a set of test scores is to be used in comparing the highest performers in a class, one might want to use a pdf,  , in which the probability of finding a certain score, f(x), is multiplied by that score:  . A mean found using the weighted pdf might be called a score-weighted mean. Find the score-weighted mean for an exam for which the probability of finding a score  is given by the function  . You will need to construct the weighted pdf then use it to find the mean score.
A) 66.7 
B) 60.0 
C) 50.0 
D) 75.0

Probability Density Functions Can Be Weighted So That Different Properties