Question

Suppose another survey in British Columbia reveals that among 180 adults with cancer, only 80 adults were abused in their childhood. Suppose again that a random sample of five adult persons is taken from this group without replacement and let denote by Y the random variable which represents the number of adults abused during their childhood period in the sample.

(a) Find the probabilities of all the possible values of Y and plot the histogram of Y . How do you compare this histogram with the histogram of X.

(b) Find the probabilities of all the possible values of Y using the formula for the binomial distribution with p = 80/180 as an approximation. Plot the histogram and compare it with the histogram obtained using the hypergeometric formula.

(c) Is the precedent approximation close enough? Why or why not?

(d) Calculate the mean and variance using both binomial and hypergeometric distributions, respectively. Provide a comparison and summarize your findings.

Answer 1

Answer is below:

y	P(Y=y)
1	0.210699
2	0.3432
3	0.273159
4	0.106228
5	0.016147

y	P(Y=y)
1	0.212154
2	0.338837
3	0.270582
4	0.108038
5	0.017255