Basic Statistics SATHYABAMA UNIVERSITY, B.Tech December 2014 Question Paper

Register Number

                               

SATHYABAMA UNIVERSITY

(Established under section 3 of UGC Act,1956)

Course & Branch :B.Tech - BIN/BME/BTE

Title of the Paper :Basic Statistics  Max. Marks:80

Sub. Code :6C0013(2008/2009)  Time : 3 Hours

Date :13/12/2014         Session :AN

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                                       PART - A  (10 x 2 = 20)

                        Answer ALL the Questions

1.     Define Skewness and Kurtosis.       

2.     If the Karl-Pearson’s Coefficient of skewness of a distribution is 0.32, its standard deviation is 6.5 and the mean is 25, find the mode.

3.     Define correlation coefficient of two random variables X and Y.

4.     What are the normal equation to estimate the values of a and b in fitting a line y = a + bx.

5.     State Baye’s theorem.

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.     Define random variable.

8.     Find E(X) where X is the outcome of a die when a die is rolled.

9.     Define Binomial distribution.

10.   If X follows Poisson distribution and P(X = 1) = 0.3 P(X = 2) = 0.2, find P(X = 0).

                                      PART – B   (5 x 12 = 60)

Answer All the Questions

11.   (a) Compute mean, median and mode for the following data:

Class	10-15	15-20	20-25	25-30	30-35	35-40	40-45	45-50
Frequency	2	28	125	270	303	197	65	10

(b) The index number of prices of two articles X and Y for six consecutive weeks is given below.

X	314	326	336	368	404	412
Y	330	331	320	318	321	330

        Find which has a more variable price?

 (or)

12.   Calculate the mean, median and variance of the following data:

Height in cm	95-105	105-115	115-125	125-135	135-145
No. of Children	19	23	36	70	52

13.   (a) Find the coefficient of correlation between industrial production and export using the following data:

Production(X)	55	56	58	59	60	60	62
Export(Y)	35	38	37	39	44	43	44

        (b) A sample of 12 fathers and their eldest sons has the following data: About their heights in inches.

Fathers	65	63	67	64	68	62	70	66	68	67	69	71
Sons	68	66	68	65	69	66	68	65	71	67	68	70

        Calculate the rank correlation coefficient.

 (or)

14.   (a) For a certain X and Y series which are correlated, the regression lines are 8x – 10y = -66, 40x – 18y = 214.

Find         (i) The correlation coefficient between them and

(ii) The mean of the two series.

(b) Fit a straight line to the following data:

X	1	2	3	4	6	8
Y	2.4	3	3.6	4	5	6

15.   (a) There are 3 true coins and 1 false coin with ‘head’ on both sides. A coin is chosen at random and tossed 4 times. If ‘head’ occurs all the 4 times, what is the probability that the false coin has been chosen and used.

        (b) From 6 positive and 8 negative numbers, 4 numbers are chosen at random(with out replacement) and multiplied. What is the probability that the product is positive?

 (or)

16.   The contents of urns I, II, III are as follows: 1 white, 2 black and 3 red balls, 2 white, 1 black and 1 red balls, 4 white, 5 black and 3 red balls. One urn is chosen at random and two balls are drawn. They happen to be white and red. What is the probability that they come from urns I, II, or III?

17.   (a) A random variables X has the following probability distribution.

x	0	1	2	3	4	5	6	7
P(x)	0	K	2K	2K	3K	K2	2K2	7K2 + K

        Find (i) the value of K,, (ii) P(1.5 < x < 4.5 / X > 2) and (iii) the smallest value of y for which Pr(X £ y) > ½.

        (b) A continuous random variable X has a probability density function f(x) = kx²e^-x; x ³ 0 Find k, mean and variance.

 (or)

18.   (a) Let X denote a random variable that takes on any of the values -1, 0, 1 with respective probabilities P(X = -1) = 0.2, P(X = 0) = 0.5, P(X = 1) = 0.3. compute E(X²).

(b) Suppose that the error in the reaction temperature in °C for a controlled laboratory experiment is a continuous random variable X having the probability density function 

(i) verify that  

(ii) find P(0 < x £ 1).

19.   (a) Find the mean and variance of Binomial distribution.

(b) Prove that Poisson distribution is the limiting case of Binomial Distribution.

 (or)

20.   (a) A random variable X follows poisson distribution and if

P(X = 1) = 2 P(X = 2),

find (i) P(X = 0)

(ii) standard deviation of X.

(b) A normal distribution has mean m = 20 and standard deviation s = 10. Find P(15 £ x £ 40).

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