Answer exactly four of the following six questions. Clearly label each response,

Question

Answer exactly four of the following six questions. Clearly label each response, and use the rest of this page and the entire next page. a. Why does correlation not imply causation? Why does extrapolating beyond the range of the data in linear regression often lead to errors? b. Explain the equally likely rule, the not rule, and the law of large numbers. c. What conditions are needed for Bernoulli trials? What is the connection between Bernoulli trials and the Binomial distribution? Give an example of a Binomial experiment. d. What is the difference between discrete and continuous random variables? How is probability calculated for discrete random variables? How is probability calculated for continuous random variables? Give one example of a Discrete Random Variable and one example of a Continuous Random Variable. e. State the Central Limit Theorem. Why is the Central Limit Theorem important?

Explanation / Answer

c) Conditions:

1) Each trial result into either success or failure.

2) Probability of success remain constant from trial to trial and denotes as p.

3) The trials are independent.

Binomial approximation to Bernoulli trials, Binom(n,p)

Mean, mu=np, standard deviation, sigma=sqrt npq.

1) Example: Suppose, 20 donors come to a blood drive, 65 of people are universal donor. What is the probbaility that exactly 2 are universal donor.

e) Central Limit Theorem: If a repeated sample sof size N are drawn from any population with mean, mu and standard deviation, sigma, then as N becomes large, the sampling distribution of sample means will approach normality, with mean mu and standard deviation, sigma/sqrt N.

CLT is important because, it remove sthe condition that the variable be normally distributed in th epopulation. Whenever sample size is large, assume sampling distribution is normal in shape with mean mu and standard deviation, sigma/sqrt N.

b) Equally likely rule:

P(E)=number of ways E can happen/Total number of events in the sample space

Law of large numbers: As the number of identically distributed, randomly generated variable increases, their sample mean sapproaches the theoretical means.

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