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Course: Statistics & Probability (3447)

Level: BS Computer Science Semester: Autumn, 2014

Total Marks: 100 Pass Marks: 50

ASSIGNMENT No. 1

(Unit 1-4)

Note: All questions carry equal marks.

Q.1 a) Discuss the primary andsecondary data along with their importance. Also describe the methods of data collection separately. (10)

b) The following data are the distribution of number of mistakes, 150 students different number of mistakes in translating certain passage from Urdu to English. Calculate different measure of central tendency and dispersions i.e. (i) Mean (ii) Standard Deviation (iii) Mode (iv) Q₁and Q₃. (10)

Number of Mistakes	Number of Students
17-19 20-22 23-25 26-28 29-31 32-34	5 63 39 24 17 2

Q.2 a) Define and explain: (10)

i) Sample point and sampleSpace ii) Event

iii) Mutually ExclusiveEvents iv) Exhaustive Events

b) Threeurns of the same appearance have the following proportions of whiteand black balls: (10)

Urn A:1 white, 2 black balls. Urn B:2 white, 1 black ball. Urn C:2 white, 2 black balls.

One of these urns is selected at random and a ball is drawn from it. It turns out to be white. What is the probability that urn C was chosen?

Q.3 a) Define and explain thecontinuous and discrete random variables. (10)

b) Let X has the following probability distribution: (10)

X	1	2	3	4	5
f(X)	0.2	0.3	0.2	0.2	0.1

Find E(X), Var(X) and probability function of 3X – 1, X²and X²+ 2. Also find E (3X – 1), E(X²) and E(X²+ 2) and interpret the results.

Q.4 a) Define and explain in detail the applications of the following distributions. (10)

i) Normal Distribution ii) Exponential Distribution

b) Given the join probability function with values f(x,y) in the following
table: (10)

Y	X 1 5 10
1 2 3	1/20 2/20 3/20 4/20 0 3/20 2/20 4/20 1/20

Find the marginal probability function for x and for y.
Calculate P(x = 5|y = 3) and P(x =10|y =1)

Q.5 a) Draw all possible distinct samples of size two from the population: 2, 4, 6, 8, 10. Calculate and verify the properties of the sampling distribution. (10)

b) Define and explain the following terms: (10)

i) Population & Sample ii) Ratio & Percentage

iii) Sampling Design & Sampling Frame iv) Parameter & Statistic

ASSIGNMENT No. 2

(Unit 5-9)

Note: All questions carry equal marks.

Q.1 a) Differentiate between: (05)

i) Simple and Composite Hypothesis

ii) Point and Interval Estimates

b) A manufacturer claimed that 90% of the machine parts that is supplied to a factory conformed to specifications. An examination of 200 such parts revealed that 168 parts are not faulty. Determine whether the manufacturer’s claim is legitimate at the 01% level of significance. (15)

Q.2 a) Explain with examples the difference between: (10)

i) Null Hypothesis and Alternative Hypothesis

ii) Acceptance Region and Rejection Region

Type-I Error and Type-II Error
Level of significance and test statistic

b) A random sample of size 36 is taken from a normal population with a known variance σ²= 25. If the mean of the sample i.e.

= 42.6, test the null hypothesis = 45 against the alternative hypothesis < 45 with a= 0.05. (10)

Q.3 a) Define and explain the terms Regression & correlation, write at least four properties of each. (10)

b) The following are the number of inquiries which a real estate agency received in eight weeks about houses prices (X) and houses for sale (Y) (10)

X	60	72	47	38	17	45	33	57
Y	82	85	62	53	29	50	69	88

Fit Y = a+ βX + εby least squares method and estimate Y for X = 50.

Q.4 a) Write a short note on multiple and partial correlation. Discuss the importance of each. (10)

b) Calculate ρ ₁₂, ρ _13.2, ρ _1.23for the following data and interpret the
result. (10)

X₁	3	5	6	8	12	14
X₂	16	10	7	4	3	2
X₃	90	72	54	42	30	12

Q.5 a) Define and explain the terms: (10)

i) Response and explanatory variables

ii) Standard error of estimates

iii) Scatter plot

Residuals

b) A sample of size 78 from a binomial population gave 35 successes. Test the null hypothesis that the true proportion of successes is 0.55 against the alternative that it is less using a= 0.05. (10)
Q:1
Discuss the primary andsecondary data along with their importance. Also describe the methods of data collection separately.
Q:2
Sample point and sampleSpace
Q:3

Follow these links

advantages and disadvantages of dispersion

Mean, Median, Mode, and Range

Random Variables: Definition, Types

& Examples

Distribution and Quantile Functions

Suppose A and B are events with

Poisson process

Course Contents Detail
Programme Name:
	Statistical Inference
	Sampling and Sampling Distributions, Estimation
	Statistical Data
	Grouping and Displaying Data (Data Arrangement, Examples of Raw Data, Data Array and frequency Distribution, Graphing Frequency Distribution) Measure of Central Tendency and Dispersion (Arithmetic Mean, Weighted Mean, Geometric Mean, Median, Mode Dispersion, Ranges, Relative Dispersion, Exploratory Data Analysis)
	Probability
	Basic Terminology in Probability, Three Types of Probability, Probability Rules, Statistical Independence, Statistical Dependence
	Special Distributions
	Random Variables, Expected Value, Binomial Distribution, Poisson Distribution, Normal Distribution, Choosing the correct Distribution
	Inference about Proportion
	Hypothesis Testing Procedure, Power of Hypothesis Test, Hypothesis Testing of Proportions
	Inference about Means
	Hypothesis Test of Mean, Hypothesis Testing for Differences between Means and Proportion, Tests for Differences between Means (Larges & Small Sample Sizes)
	Chi-Square & Analysis of Variance

	Simple Linear Regression and Correlation
	Estimation using the Regression Line, Correlation Analysis
	Quality and Quality Control
	Statistical Process Control, Control Charts for Process Means, Variability and& Attributes, Total Quality Management, Acceptance Sampling	Statistical Inference

Allama Iqbal Open University | Islamabad

Solved papers aiou-statistic and probability -code No 3447-Autumn 2014

Solved papers

Solved papers aiou--statistic and probability -code No 3447-Autumn 2014

Outline 3447

(5) Data Arrangement,

(6) Examples of Raw Data,

(7) Data Array and frequency Distribution,

(8) Graphing Frequency Distribution

(9) Arithmetic Mean,

(10) Weighted Mean,

(11) Geometric Mean,

(12) Median, Mode

(13) Dispersion,

(14) Relative Dispersion,

(15) Exploratory Data Analysis

(16) Basic Terminology in Probability,

(17) Three Types of Probability,

(18) Probability Rules,

(19) Statistical Independence,

(20) Statistical Dependence

(21) Random Variables,

(22) Expected Value,

(23) Binomial Distribution,

(24) Poisson Distribution,

(25) Normal Distribution,

(26) Choosing the correct Distribution

(27) Hypothesis Testing Procedure,

(28) Power of Hypothesis Test

(29) Hypothesis Testing of Proportions

(30) Hypothesis Test of Mean,

(31) Hypothesis Testing for Differences between Means and Proportion,

(32) Tests for Differences between Means (Larges & Small Sample Sizes

(33 chi-Square as Tests of Independence,

(34) Goodness of Fit and Distribution Shapes,

Estimation using the Regression Line,

Quality and Quality Control

Control Charts for Process Means,

Course: Statistics & Probability (3447)

Level: BS Computer Science Semester: Autumn, 2014

Total Marks: 100 Pass Marks: 50

papers

when r=-1,0 and +1

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