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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
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MCA I Semester Examinations, October/ November - 2020
COMPUTER ORIENTED STATISTICAL METHODS
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Time: 2 Hours--- Content provided by FirstRanker.com ---
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Max.Marks:75
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Answer any five questions
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All questions carry equal marks----
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1.a)
A random variable X has the following probability function.
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x
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01
2
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3
4
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56
7
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2
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f (x) kk
k
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2k
3k
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2k
2
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2k
7k k
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Determine
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(i) k
(ii) Evaluate (
p x )
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6 , (
p x )
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6 and p 0( x )
5
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used
(iii) Mean and Variance
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b) In a poker hand consisting of 5 cards, find the probability of holding 2 aces and 3jacks.--- Content provided by FirstRanker.com ---
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[10+5]
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2.a)In a certain assembly plant, three machines, B1, B2, and B3, make 30%, 45%, and 25%,
respectively, of the products. It is known from past experience that 2%, 3% and 2% of
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the products made by each machine, respectively, are defective. Now, suppose that afinished product is randomly selected. What is the probability that it is defective? If it is
defective find the probability that it is from
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i) B1 ii) B2 iii) B3
b) State and prove Bayes theorem.
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[10+5]3.
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Two ball point pens are selected at random from a box that contains 3 blue pens, 2 red
pens, and 3 green pens. If X is the number of blue pens selected and Y is the number of
red pens selected, find
a) The joint probability function f (x, y),
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b) P [(X, Y ) A], where A is the region {(, )| + 1}.c) The covariance of X and Y.
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[15]4.
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Fit the binomial distribution
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[15]x
0
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1
2
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34
5
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f
2
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1420
34
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22
8
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S OCT 2020
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5.a)
If X is a normal variate with mean 30 and standard deviation of 5. Find the probabilities
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that i) 26 40 ,ii) 45 ,
iii) 22.
b)
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Find i) ( < 2.365) when = 7 degrees of freedom
ii) ( > 1.318) when = 24 degrees of freedom
iii)(-1.356 < < 2.179) when = 12 degrees of freedom.
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[8+7]
6.
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An experiment was performed to compare the abrasive wear of two different laminated
materials. Twelve pieces of material 1 were tested by exposing each piece to a machine
measuring wear. Ten pieces of material 2 were similarly tested. In each case, the depth
of wear was observed. The samples of material 1 gave an average wear of 85 units with
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a sample standard deviation of 4, while the samples of material 2 gave an average of 81with a sample standard deviation of 5. In testing for the difference in the abrasive wear
of the two materials, we assumed that the two unknown population variances were
equal. Were we justified in making this assumption? Use a 0.10 level of significance.
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[15]
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used
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7.A pair of dice are through 360 times and the frequency of each sum is indicated below
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Sum
2 3
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45
6
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7
8
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910 11 12
Frequency 8 24 35 37 44 65 51 42 26 14 14
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Would you say that the dice are fair on the basis of the chi-square test at 0.05 level of
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significance?--- Content provided by FirstRanker.com ---
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[15]
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8.
Calculate the linear regression of Y on X from the data given below. Taking deviation
from actual means of X and Y. Estimate the likely demand when price is Rs. 20. [15]
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X
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1012
13
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14
16
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15Y
40
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38
43
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4537
43
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---oo0oo---
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