of 20 classes: 16 have 25 students 3 have 100 students 1 has 300 students select

Question

of 20 classes: 16 have 25 students 3 have 100 students 1 has 300 students select a student randomly from the 1000 students. Let therandom variable x equal the size of the class the student belongs,define the p.m.f. of x find the E(x), expected value of x of 20 classes: 16 have 25 students 3 have 100 students 1 has 300 students select a student randomly from the 1000 students. Let therandom variable x equal the size of the class the student belongs,define the p.m.f. of x find the E(x), expected value of x

Explanation / Answer

The total number of students is 25(16)+100(3)+300 = 1000students The probability mass function is simply the probability that thestudent is in a given class. These are given below: Probability of being in one of the 25-student classes: (25*16)/1000 = 400/1000 = .40 Probability of being in one of the 100-student classes: (3*100)/1000 = 300/1000 = .30 Probability of being in the 300-student class: (300/1000) = .30 That is: P(25) = .40 P(100) = .30 P(300) = .30 E(X) is simply the expected number of students in the class. This is calculated by weighting the probabilities with the numberof students in each class: E(X) = (.4)(25) + (.3)(100) + (.3)(300) = 10 + 30 + 90 = 130 FINAL ANSWERS: P(25) = .40 P(100) = .30 P(300) = .30 E(X) = 130

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