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 Ques

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………………………………..………………..…………………… 3
Question 4………………..……………………………………..……………… 4
Question 5……………………………………………………………………… 4
Question 6……………………………………………………………………… 4

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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: [2+3+4+1 Marks] The following are the closing prices (in dollars) of two stocks on five consecutive Fridays:
Stock A: 18.25 17.03 18.41 17.44 18.10
Stock B: 20.31 20.27 19.55 20.60 20.40

Calculate the mean, median for stock A and stock B.
Compute the range and the inter-quartile range for each stock.
Calculate the standard deviation for each group.
Which set is less variable?
Q-2: [8 +2Marks]
i) In how many 5-digit numbers can be formed from the 10 digits (0-9), if
Repetitions are allowed ;
The numbers begin with 40;
The numbers are even;
The numbers are divisible by5.
ii) How many different sets of 4 students can be chosen out of 17 qualified students to represent a school in a mathematics contest?
Q-3: [3+3+4 Marks] A cereal company has been running a radio advertisement for a new cereal. A marketing research firm determined that probability that an individual has heard the advertisement is 0.5, the probability that an individual bought the cereal is 0.2 , and the probability that an individual has heard the advertisement and bought the cereal is 0.1.

What is the probability that an individual will purchase the product, given that the person has heard the advertisement?
What is the probability that an individual has heard the advertisement, given that the person purchased the product?
Are the two events, the person purchased the product, and an individual has heard the advertisement independent events? Justify your answer.

Q-4: [5+5 Marks] a) Among the 78 doctors on the staff of a hospital, 64 carry malpractice insurance, 36 are surgeons, and 34 of the surgeons carry malpractice insurance. If one of these doctors is randomly chosen by lot to represent the hospital staff at an A.M.A. convention, what is the probability that the one chosen is not a surgeon and does not carry malpractice insurance? .

b)Given p(A)=0.59, p(B)= 0.30, and p(A∩B)=0.21. find
i) p(A∪B)
ii) p( A∩ (B ) ̅)
iii) p((A ) ̅ ∪ (B ) ̅)
iv) p( (A ) ̅∩ B ̅)
Q-5: [3+2+2+3 Marks] Suppose that the random variable X has the following cumulative distribution function:
x -1 1 3 5
F(x) 1/4 1/2 3/4 1

Find the probability distribution of this random variable.
Find p(x<3),p(x ≥1 )
Find the mean of the random variable X.
Find the standard deviation of the random variable X.
Q-6: [3+4+3 Marks] The cumulative distribution function of the random variable X is given by:

Find the probability density function for the random variable X.
compute p(X≤ 5) and p( 8< X )
Find the expected value for the random variable X.