Please answer Question 2 only. Question 1 has been answered, but need to compare answers from...

Please answer Question 2 only.

Question 1 has been answered, but need to compare answers from Question 2 with Question 1.

Child-abuse victims and developing cancer: Truth or myth? Is physical childhood abuse somehow related to the development of cancer later in life? A recent survey revealed that people who have been physically abused as children were 49% more likely to develop cancer as adults.

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1. Suppose in a region in Saskatchewan, among a group of 20 adults with cancer, seven were physically abused during their childhood. A random sample of five adult persons is taken from this group. Assume that sampling occurs without replacement, and the random variable X represents the number of adults in the sample who were abused during their childhood period.

(a) Write the formula for p(x), the probability distribution of X. How this distribution is called?

(b) Using the adequate formulas, find the mean and variance of X?

(c) Find the probabilities of all the possible values of X. Plot the histogram of X and try the locate the approximative value of the mean µ.

(d) What is the probability that at least one person was abused during childhood?

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2. 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.

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

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