Download MUHS BPTH Final Year 2019 Summer 51411 Musculoskeletal Physiotherapy 2019 Summer Question Paper

Code: 20AC03T

II B. Tech I Semester (R20) Regular Examinations Nov-Dec 2021

PROBABILITY AND STATISTICS

(Common to CSE, IT, CSE(AI), CSE(DS), CSE(CY), CSE(IOT))

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Time: 3 Hours

Max. Marks: 70

Note: 1. Question paper consists of two parts A and B.

2. Part A is compulsory, answer any four questions from Part B.

PART-A (14 Marks)

1. Answer the following short answer type questions.

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1. (a) If P(A)=1/2, P(B)=1/3, P(AnB)=1/4, then find P(A/B).
2. (b) Define Random variable.
3. (c) Define Poisson distribution.
4. (d) Define Null hypothesis.
5. (e) Write properties of t-distribution.

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6. (f) Define type-I and type-II errors.
7. (g) Define control charts.

PART-B (56 Marks)

Answer any four questions from the following. Each question carries 14 marks

1. 2. (a) State and prove Baye's theorem. [7M]
2. (b) Two dice are thrown. Let X assign to each outcome (a,b) the number a+b. Determine the probability distribution of X. [7M]

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3. 3. A random variable X has the following probability function: [14M]

   X	0	1	2	3	4	5	6	7
   P(x)	0	k	2k	2k	3k	k2	2k2	7k2+k

   (i) Find k (ii) Evaluate P(X<6), P(X=6) (iii) If P(X=k) > 0.5, then determine the minimum value of k.

4. 4. (a) Out of 800 families with 4 children each, how many families would be expected to have (i) 2 boys and 2 girls (ii) at least one boy (iii) no girl (iv) all girls? Assume equal probabilities for boys and girls. [7M]
5. (b) Fit a Poisson distribution to the following data: [7M]

   x	0	1	2	3	4
   f	200	270	100	20	5

6. 5. (a) A population consists of the five numbers 2, 3, 6, 8 and 11. Consider all possible samples of size 2 which can be drawn without replacement from the population. Find (i) The mean of the population. (ii) The standard deviation of the population. (iii) The mean of the sampling distribution of means. (iv) The standard deviation of the sampling distribution of means. [7M]

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7. (b) State Central Limit Theorem. [7M]
8. 6. (a) A sample of 100 dry battery cells tested to find the length of life produced the following results: x = 12 hours, s = 3 hours. Assuming the data to be normally distributed, what percentage of battery cells are expected to have life (i) more than 15 hours (ii) less than 6 hours (iii) between 10 and 14 hours. [7M]
9. (b) Explain (i) Point estimation (ii) Interval estimation. [7M]
10. 7. (a) A manufacturer claims that at least 95% of the equipment which he supplied to a factory conformed to specifications. An examination of a sample of 200 pieces of equipment revealed that 18 were defective. Test his claim at 5% level of significance. [7M]
11. (b) Two random samples are drawn from two populations and their values are as follows: [7M] Sample 1: 66 67 75 76 82 84 88 90 92 Sample 2: 64 66 74 78 82 85 87 92 93 95 97 Test whether the two samples are drawn from the same normal population.

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12. 8. (a) Explain the terms attribute and control chart for attributes. [7M]
13. (b) The following data gives the number of defects in 10 machines. [7M]

    Machine No.	1	2	3	4	5	6	7	8	9	10
    No. of Defects	12	15	14	10	15	16	18	15	14	12

    Draw control chart for number of defects and comment on the state of control.

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