JNTUH MCA 2nd Sem Last 10 Years 2023-2013 Question Papers R20-R09 || Jawaharlal nehru technological university
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Code No: F3104 R09
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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
MCA I Semester Examinations, June/July - 2018
PROBABILITY AND STATISTICS
Time: 3hrs Max.Marks:60
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Answer any five questions
All questions carry equal marks
- a) A sub-committee of 6 members is to be formed out of a group consisting of 7 men and 4 women. Calculate the probability that the sub-committee will consist of (i) exactly 2 women and (ii) at least one women.
b) A, B and C wash 50%, 30% and 20% of the cars in a service station respectively. They fail to clean the glass in 5%, 7 % and 3% of the cars respectively. The glass of a washed car is checked. What is the probability that the glass has been cleaned? [6+6] - a) A random variable X takes the values 1, 2, 3,.....and P(X =n)=1/2n, n=1,2,3,.... Find (i) P(X is odd) (ii) P(X <5) (iii) P(X is divisible by 5).
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b) A fair dice is rolled 5 times. Find the probability that 1 shows twice, 3 shows twice and 6 shows once. [6+6] - a) Determine the binomial distribution for which the mean is 4 and variance is 3. Also find P(X =15).
b) Let X be normally distributed with mean 8 and standard deviation 4. Find 1) P(8<X<10) ii) P(10<X<15) iii) P(X=15). [6+6] - a) An insurance company has 25,000 automobile policy holders. If the yearly claim of a policy holder is a random variable with mean 320 and standard deviation 540, approximate the probability that the total yearly claim exceeds 8.3 million.
b) Let X1, X2, ... Xn is an random sample from the population with respect to density function. f(X)= T/x2 for x > T. Show that X is an unbiased estimator of T. Suggest an unbiased estimator of T. [6+6] =0 otherwise - a) A random sample of 200 tins of coconut oil gave an average weight of 4.95 kgs with a standard deviation of 0.21 kg. Do we accept the hypothesis of net weight 5 kgs per tin at1% level?
b) A sample of 10 house owners is drawn and the following values of their incomes are obtained. Mean Rs. 6,000; standard deviation Rs 650. Test the hypothesis that the average income of house owners of the town is Rs. 5,500. [6+6] - a) Time taken by workers in performing a job are given below.
Method I | 20 16 26 27 23 22
Method II | 27 33 42 35 32 34 38--- Content provided by FirstRanker.com ---
Test whether there is any significant difference between the variances at 5% level of significance of time distribution.
b) A sample analysis of examination results of 500 students was made. It was found that 220 students have failed, 170 have secured a third class, 90 have secured a second class and the rest, a first class. Do these figures support the general belief that the above categories are in the ratio 4: 3: 2:1 respectively? [6+6] - a) Fit a straight line to the following data:
Year: 1969 | 1970 | 1971 | 1972 | 1973 | 1974 | 1975 | 1976
Sales(in lakhs of Rs.): 38 40 65 72 69 | 60 87 95--- Content provided by FirstRanker.com ---
b) A fair die is rolled n times. Let X be the number of 1's observed. let Y be the number 2's be observed. Find Cov(X,Y) and ?(X,Y). [6+6] - Find the rank correlation coefficient for the following data:
X 92 89 87 86 86 77 71 63 53 50
y 86 83 91 77 68 85 52 82 37 57 [12]
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