Question

Question 1. Suppose that a professor chooses a random student in a class of 40 students (there are 23 girls and 17 boys in the class) to perform a calculation on the board. The professor repeats this procedure 15 times, choosing a new student each time (i.e. no student will go twice). Let X be the total number of boys chosen. Calculate the mean and variance of x. Hint 1: Use indicator random variables X; = if a boy is chosen for calculation i else. Hint 2: Notice that the distribution of X; does not depend on i.

Answer 1

from the observed data liven 40 students 23 are girls 11 ош Боу 15 times of selection Therefore x be a random variable x = number of boys choosen that 4. 0, 1, 2, .. o wP 54 х ... 23 Сб. 40с. 15 +р пс, 4 23 14 40 15 х: і, ер Тех 15с; | 23 15- і 15 (4) : 40cs іх та x 230 чо cs 15 x x тx 25 C6 40C5 с(?) - Ф., F(x) : ma *х пет » 23 е ..

where P(x=R) - ( Monte) (@ where N = 40 m 17 kui and n= 15 i f(x) = 17885 .51 40 : varlx) mo (N-m) (N-nl N2 (N-1) 40x15 ( 40-17) (40-15) 402 ( 40 -1) MY 2.349 :: var (x) = 2.349 I hope this answer will helpful please give up- vore to you