Problem Set 2

  1. You are given the following 10 observations on two variables X and Y.

X / 1 / 5 / 6 / 4 / 2 / 8 / 9 / 1 / 6 / 8
Y / 8 / 15 / 20 / 12 / 10 / 20 / 26 / 5 / 18 / 26

(a)Develop a scatter diagram for the relationship between X and Y.

(b) According to the scatter diagram, what relationship, if any, appears to exist between X and Y?

(c ) Compute the sample covariance.

(d) Interpret the meaning of the sample covariance that was found in (c).

(e) Compute the coefficient of correlation.

  1. A student at a local college just completed 15 credit hours. His grade report is presented below.

Course / Calculus / Biology / English / Music / Statistics
Credit Hours / 4 / 4 / 3 / 2 / 3
Grades / 70 / 90 / 60 / 80 / 90

Compute this student’s semester grade point average.

  1. You are given the following information on Events A, B, C, and D.

(a)Compute .

(b)Compute .

(c)Compute .

(d)Compute the complement of C, .

(e)Are A and B mutually exclusive? Explain.

(f)Are A and B mutually independent? Explain.

(g)Are A and C mutually exclusive? Explain.

(h)Are A and C mutually independent? Explain.

  1. The following are the data on the gender and marital status of 200 customers of a company.
Male / Female
Single / 20 / 30
Married / 100 / 50

(a)What is the probability of finding a single female customer?

(b)What is the probability of finding a married male customer?

(c)If a customer is female, what is the probability that she is single?

(d)What percentage of customers is male?

(e)If a customer is male, what is the probability that he is married?

(f)Are gender and martial status mutually exclusive?

(g)Is martial status independent of gender? Explain.

5.

(a) Show that

,

where is the population mean of and ais any number.

(b)50 students are randomly selected.

What is the probability of one student’s birthday being today?

What is the probability of two students’ birthday being today?

What is the probability of at least two students’ birthday being the same day?

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