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(Established under
section 3 of UGC Act, 1956)
Course & Branch: B.Tech -
BTE/BME/BIN
Title of the Paper: Basic
Statistics Max.
Marks: 80
Sub. Code: 5ET102B-6C0013
(2006/07/08/09) Time: 3 Hours
Date: 11/12/2010 Session:
AN
______________________________________________________________________________________________________________________
PART
- A (10 X 2 = 20)
Answer ALL the Questions
1. State the empirical relationship between the averages.
2. Write Bowley’s coefficient of skewness.
3. Write probable error in the correlation coefficient.
4. Write the correlation formula for tied ranks.
5. The
letters of the word “REGULATIONS” be arranged at random. What is the chance
that there are exactly 4 letters between R and E?
6. From
a pack of 52 cards 3 cards are drawn at random find the chance that they are
king, queen and a knave.
7. A
continuous random variable has the probability
function f(x) = Ax2, 0 £ x £ 1. Find A,
also find the probability that x lies between 0.2 and 0.5.
8. Write
the general form of marginal and conditional distributions in the case of
continuous functions.
9. Comment: the mean of binomial distribution is 3 and variance 4.
10. If
x is a Poisson variate such that p(x = 2) = 9p(x=4) + 90p(x = 6) Find l.
PART – B (5 x 12 = 60)
Answer All the Questions
11. (a) Find the median and two quartiles.
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Marks
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below
10“
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20“
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30“
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40“
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50“
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60
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below
70
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Freq.:
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15
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35
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60
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84
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106
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120
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125
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(b) In an experiment the mean and standard deviation
of 20 observations are 25 and 10 respectively.
Later it was found that one entry was wrongly recorded as 34 instead of
44. Calculate the correct mean and
standard deviation.
(or)
12. (a)
Find out the missing frequencies. The arithmetic mean is 67.45
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Height
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60 - 62
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63 - 65
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66 - 68
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69 - 71
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72 - 74
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total
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Value
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5
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18
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f3
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f4
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8
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100
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(b) Calculate mean deviation about mean.
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Interval
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20 - 30
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30 - 40
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40 - 50
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50 – 60
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60 – 70
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70 – 80
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80 – 90
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90 – 100
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Freq.:
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3
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8
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9
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15
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20
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13
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8
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4
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13. Fit a parabolic curve.
X: 1 2 3 4 5 6 7 8 9
2
6 7 8 10 11 10 9
(or)
14. (a) Calculate the coefficient of correlation.
X: 1 3 5 8 9 10
Y: 3 4 8 10 12 11
(b) In partially destroyed records the following data
available. Variance of x is 25, regression equation x on y is 5x – y = 22,
regression equation y on x is 64x – 45y = 24.
Find mean values of x and y, coefficient of correlation, standard
deviation of y.
15. (a)
Three groups of children contains respectively 3 girls and 1 boy, 2 girls and 2
boys and 1 girl and 3 boys. One child is
selected at random from each group. Find
the chance that the three selected consists of 1 girl and 2 boys.
(b)
Three boxes contains 1 white, 2 black and 3 red balls, 2 white, 1 black and 1
red ball, 4 white, 5 black and 3 red balls respectively. One box is selected at random and two balls
are drawn. They happen to be white and red.
What is the probability that they came from box 1
(or)
16. (a)
In a bolt factory machines A,B and C manufacture 25%, 35%, 40% of the total. Of their output 5,4,2 per cent
defective. A bolt is drawn at random and
found to be defective. What is the
probability that is was manufactured by machines A,B, and C.
(b) Box A contains 2 white 1 black and 3 red
balls. Box B contains 3 white 2 black and 4 red balls. Box C contains 4 white 3 black and 2 red
balls. One box is selected at random and two balls are drawn, they are red and
black. What is the probability that both
balls came from box B?
17. (a)
A the diameter of an electric cable say X is assumed to be a continuous random
variable with pdf f(x) = 6x (1 – x) 0 £ x £ 1, find 1. Check that it is pdf. 2. Determine the number b such that
p(X < b) = p (X> b).
(b)
The joint probability density function of a two dimensional random variable
(X,Y) is given by f(x,y) = 2,0 < x < 1,0<y<x,= 0 otherwise. Find
the marginal density functions of X and Y. Find the conditional density
function of Y given X = x and conditional density function of X given Y = y.
(or)
18. (a)
If X and Y are two random variables having joint density function f(x,y) = 1/8
* (6-x-y); 0 <x<2, 2<x<4 = 0 otherwise. Find p(X<1 È Y<3), P(X+Y<3), p(X<1/Y<3).
(b) A petrol pump is supplied with petrol once a
day. If its daily volume X of sales in
thousands of liters is distributed by f(X) = 5(1-x)4, 0 £ x £ 1 what must be the capacity of its tank in order that its supply will
be exhausted in a given day shall be 0.01?
19. (a)
An irregular six faced die is thrown and the expectation that in 10 throws it
will give five even numbers is twice the expectation that it will give four
even numbers. How many times in 10,000
sets of 10 throws each would you expect it to give no even number?
(b)
A manufacturer of cotter pins knows that 5% of his product is defective. If he
sells cotter pins in boxes of 100 and guaranties that not more than 10 pins
will be defective, What is the
approximate probability that a box will fail to meet the guaranteed quality?
(or)
20. (a) If X is
a normal variate with mean 30 and SD 5, Find the probabilities that i. 26 £ X £ 40, ii. X ³ 45 and |X – 30| > 5. (4)
(b)
In an examination it is laid down that a student passes if he secures 30% or
more marks. He is placed in the first, second or third division according as he
secures 60% or more marks, between 45% and 60% and between 30% and 45%
respectively. He gets distinction in case he secures 80% or more marks. From the result that 10% students failed in
the examination, whereas 5% of them obtained distinction, Calculate percentage
of students placed in the second division.
(Assume the distribution is normal). (8)
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