Course Code: M130

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Course Code: M130

مُساهمة  whatsapp::00966542495275 في الثلاثاء سبتمبر 30, 2014 3:59 am

Faculty of Computer Studies
Course Code: M130
Course Title: Introduction to Probability and Statistics
Tutor Marked Assignment

Cut-Off Date: Total Marks:60

Contents
Question 1……………………..………………………………………..……… 3
Question 2……………………………..………………..……………………… 3
Question 3………………………………..………………..…………………… 4
Question 4………………..……………………………………..……………… 4
Question 5……………………………………………………………………… 5
Question 6……………………………………………………………………… 5

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QUESTION 1 2 3 4 5 6
MARK 10 10 10 10 10 10
SCORE
TOTAL




Tutor’s Comments:


The TMA covers only chapters 1, 2, 3 and 4. It consists of six questions for a total of 60 marks. Please solve each question in the space provided. You should give the details of your solutions and not just the final results.

Q−1: [3+2+2+3 Marks] The following data represent salaries (in dollars) from a school district in Greenwood, South Carolina.
10,000 11,000 11,000 12,500 14,300 17,500 18,000 16,600 19,200 21,560 16,400 107,000
First, assume you work for the school board in Greenwood and do not wish to raise taxes to increase salaries. Compute the mean, median, and mode, and decide which one would best support your position to not raise salaries.
Second, assume you work for the teacher union and want a raise for the teachers. Use the best measure to support your position.(refer to part a)
Find the interquartile range.
Find the sample standard deviation.


Q-2: [3+2+3+2 Marks]
In how many ways can a committee consisting of three men and two women be chosen from seven men and five women?
How many committee of five with a given chairman can be selected from twelve persons?
In how many ways can a teacher choose one or more students from six eligible students?
Find the number of permutations that can be formed from the letters UNUSUAL?

Q-3: [4+4+2 Marks] The medal distribution from the 2008 Summer Olympic Games for the top 23 countries is shown below.



Gold Silver Bronze
United States 36 38 36
Russian 23 21 28
China 51 21 28
Great Britain 19 13 15
Others 173 209 246

Choose one medal at random.
Find the probability that the winner won the gold medal, given that the winner was from United States.
Find probability that the winner was from United States, given that she or he won a gold medal.
Are the events “medal winner is from United States” and “ gold medal won” independent? Explain.

Q-4: [3+3+4Marks] A shipment of two boxes A1 and A2, each containing six telephones, is received by a store. Box A1 contains one defective phone, and box A2 contains two defective phones. After the boxes are unpacked, a phone is randomly selected :
What is the probability that it is defective?
What is the probability that it is not defective?
Find the probability that it came from box2.
Q-5: [3+2+4+1 Marks] The probability that a cellular phone company Kiosk sells x number of new phone contracts per day is shown below.
X 4 5 6 8 10
P(X)=F(X) 0.4 0.3 0.1 0.15 0.05


Find The cumulative distribution of the random variable x .
Find the mean of the random variable X.
Calculate the variance and standard deviation of the random variable X.
What is the probability that they will sell 6 or more contracts.



Q-6: [2+2+2+2+2 Marks] Let f(x) = 3x^(-4) x≥1

Show that f(x) is the probability density function of some random variable x.
Find the cumulative distribution function F(x) of x.
Compute p(x ≤ 4) , and p(x >4)
Find the mean of the random variable x.
Find the standard deviation of the random variable x.

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