Download DBATU B.Tech 2019 March 4th Semester Probability and Statistics Question Paper

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DR. BABASAHEB AMBEDKAR TECHNOLOGICAL UNIVERSITY, LONERE

Mid Semester Examination - March 2019

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Course: B. Tech Computer science

Subject Name: Probability & statistics

Sem: IV

Date:-12-03-19

Max Marks: 20

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Duration:-1 Hr.

Subject Code: BTCOC402

Instructions to the Students:

1. All questions are compulsory
2. Use of Non-programmable calculator is allowed.

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3. Figures to the right indicate full marks.

Q.1 Multiple choice questions

1. Given that P(A) = 0.8, P(B) = 0.7, P(AUB) = 0.9, what is P(AnB)
   A. Can be any number between 0 and 0.7
   B. 0.1
   

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   C. 0.06
   D. 0.6
2. X takes values 1,2,3 with P(X=1)=0.2 and E(X) = 2.2, then P(X=2) is .......
   A.0.5
   B. 0.56
   

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   C. 0.3
   D. 0.4
3. If random variable X has binomial distribution with parameter n and p, then
   A. Mean < Variance
   B. Mean > Variance
   

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   C. Mean = Variance
   D. Mean = Variance
4. Suppose X follows normal distribution with mean 60 and variance 10, then maximum height of its probability density curve is of........
   A. 60
   B. 50
   

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   C. 65
   D. 70
5. The probability of drawing one white ball randomly from a bag containing 6 red, 8 black, 10 yellow and 1 green ball is
   A.1/25
   B. 0
   

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   C. 1
   D. 14/25
6. The sample space is......
   A. A set of the data space in which a sample experiment can be performed
   B. The set of an possible outcome of a random experiment
   

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   C. A space from which a sample for study may be drawn
   D. None

(Level/CO) Marks

1-2 6

Q.2 Solve Any Two of the following.

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1. In a bolt factory, machine A, B, C manufacture respectively 25%, 35% and 40% of the total, of their output 5, 4, 2 percent are known to be defective bolts. A bolt is drawn at random from the product and is found to be defective. What are the probability that it was manufacture by i) machine A ii) machine B or C
   (3X2)
2. Two beads are selected at random without replacement from a bowl containing 4 blue, 1 red and 2 black beads. Let X denote the number of red beads, Y denote the number of black beads drawn.
   1. Find the joint p.m.f
   2. Obtain the marginal p.m.f of X and Y
   3. Calculate P(X<Y)

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3. An unbiased coin is tossed six times find the probability of getting
   1. Two heads
   2. at least four heads

Q.3 Solve Any Two of the following.

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1. Suppose continuous random variable X has p.d.f
   f(x) = x²/3; -1= X =2
   = 0; Otherwise
   If A = {xlx = 0}
   B = {x}-1/2 = x = 1/2}
   

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   Find P(A),P(B), P(A'), P(AnB), P(AUB), P(A'UB'),P(AnB)
2. A die is tossed twice. Getting a number greater than 4 is considered a success. Find the mean and variance of the probability distribution of the number of successes.
3. Fit a binomial distribution to the following data:
   X: 0 1 2 3 4
   f: 28 62 46 10 4

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