Question

Directions: Each problem below describes an experiment and defines a random variable. For each problem: (a) Find the distribution of the random variable (and provide it as a chart) (b) Calculate the expected value of the random variable Do not round values. 1. A room has 15 art majors and 10 science majors. Two students are selected randomly (without replacement). Let S be the number of science majors that will be drawn.

Answer 1

1) here as experiment is done without replacement ; this is hypergeometric distribution

with paramter N =15+10 =25 ; G =10 and n=2

below is pmf of S :

P(S=s) =$\binom{15}{2-s}\binom{10}{s}/\binom{25}{2}$   

s	P(s)
0	0.35
1	0.5
2	0.15

P(s) 0.6 0.5 0.3 0.2 0.1 P(s)

also from Hypergeometric distribution expected value E(x) =nG/N =2*10/25=0.8