FAISALABAD BOARD 2012
PAPER STATISTICS PART-I
Time: 20 Minutes
(objective Part)      
Marks:17

Note: Four Answers are given against each column A,B,C&D. Select the write answer and only separet answer sheet, fill the circle A,B,Cor D with pen or marker in front of that question number.

• In hypergeometric distribution, k is called the numbers of in the population.
  

(a) Failures
(b) Successes
(c) Parameters
(d) None

• The S.D. of binomial distribution is:

(a) np  
(b) nq  
(c) np(1— p)  
(d) nP

• The trials in the binomail experiment are:

(a) Dependent
(b) Independent
(c) Biased       
(d) Unbiased

• E(kx) is equal to, when k is constant:

(a) E(x)           
(b) x E(k)
(c) k E(x)        
(d) k2K(x)

• v(x-y) is equal to:

(a) v(x)+v(y)   
(b) v(x)-v(y)
(c)
(d)

• Three dice are polled, then numbers of sample points in sample space is:

(a) 6    
(b) 36  
(c) 216
(d) 1296

• nC0 is equal to:

(a) nP0 
(b) nP0 
(c) nC1 
(d) nC2

• Consumer price index number are:

(a) Un-weighted         
(b) Weighted
(c) Simple       
(d) Quantity

• Which average is the most suitable for chain index numbers?

(a) A.M.         
(b) Median
(c) H.M.         
(d) G.M.

• m2 is equal to:

(a) µ    
(b) S2  
(c) S    
(d) σ

• If s S = 6.8837 ,  = 97.8833 , then C.V. is:

(a) 6.04%
(b) 8.04%
(c) 9.04%        
(d) 7.03%

• v(y - a) is equal to:

(a) v(y)
(b) v(y)-v(a)
(c) v(y) + v(a) 
(d) Zero

• If a = 98 , ∑ D = 2 and n =10, then  is:

(a) 97.73         
(b) 97.83         
(c) 90.20         
(d) 90.25

• If x = a , then x is equal to:

(a) Zero          
(b) a    
(c) 1    
(d) x

• The difference between maximum and minimum value in the data is equal to:

(a) h    
(b) f    
(c) R
(d) Y

• 1 + 3.3 log (n) is equal to:

(a) r     
(b) f    
(c) h
(d) c

• Short hand notation for product is:

(a) µ
(b) π
(c) ∑
(d)

Time: 2:40 Hours 
(Subjective Part) 
Marks: 68
SECTION-1

2. Write short answers of any Eight Parts.  16

• Define Statistics as a discipline of science.
• Distinguish between variable and constant.
• Define mode with formula.
• If ∑ x – 34|=18 and ∑|x – 35|=17.5, what is median and why?
• Write any two properties of A.M.
• Why is difficult to calculate geometric mean for
  (a) 0,4,8           (b) 3,5,-2,1
• If x1 = 2 and x2 = 8 show that AM > GM.
• Define fixed base method in index number.
• What is cost of living index number?
• Given w = 10, 15, 25, 30 and I=x100= 100, 105, 108,110,  find cunsumer price index number.
• If link relative are 90, 110, 102, 105, 115, 112, find chain indices.
• Given P1Po= 670 ,.∑ popo = 410, find base year weighted index number.

3. Write short answers of any Eight Parts. 16

• What do you understand by an array?
• Define relative frequency.
• What do you understand by dispersion?
• Distinguish between absolute and relative measure of dispersion.
• If var(x) = 5 and var (y) = 2 , then find var(2x - 3y) = ?
• If range of a series is 46 and smallest value of the series is 10, then find the maximum number in the series.
• Define kurtosis.
• What will be the shape and name of the distribution for which mean > median > mode.
• Define exhaustive events.
• Define P(a) = 0.2 , P(b) = 0.4 and P(A/B) = 0.375 then find P(AB) .
• Distinguish between simple and compound events.
• Define conditional probability.

4. Write short answers of any Six Parts.        12

• Write down the properties of probability distribution.
• Given E(2x) = 10 and E(2x)2 = 500 determine S.D.(x).
• Two coins are tossed. Let x = number of heads. Find the probability
• distribution of x.
• How the random numbers are generated?
• Given E(x) = 0 and E(x)2 = , find E(2x2 - 3x + 5) .
• If the pi Probability that it is a fine day is 0.60, find the expected number or fine days in a weak and the standard deviation.
• Define binomial probability distribution.
• Define hypergeometric random experiment.
•  If N = 40, n = 5 and k = 4, then find the mean and variance of the hypergeometric distribution

SECTION-II: Attempt any THREE questions. Each question carries 8 marks.
5.
(a)  A variable Y is determined from a variable X by the equation Y = 14 - 5X find Y when X = -3,-2,-1,0,1,2,3,4,5 and show that =14-5X.            04
(b) Following data have been obtained from a frequency distribution of continuous variable X after making the substitution U      

Compute G.M. of the variable X.         04

6.
(a)

(b) The second moment about the mean of three symmetrical disrticutions is 9, 16 25. While the fourth moment about means are 230, 780 and 1875. Discuss the types of distribution.                              04
7.
(a) For the data given find index number taking:
(i) 1936 as base year
(ii) 1938 as base year       04

b) Two cards are drawn at random from the well shuffled pack of 52 cards. Find the probability that:
(i) One is King and other is Jack.       
(ii) Both are same colours.                 04

8.
(a) A random variable ‘x’ has the following probability distribution:

Find
(i) k        
(ii) E(x)           
(iii) P(x < 4)                                       04

(b) A continuous random variable x has probability density function giving
f(x) = cx for 0    < x < 2. Find
(i) c
(ii) P (l< x <1.5)                        04

9.
(a) A pesticide was tested by applying it in the form of a spray to 50 samples of 5 files. The number of dead files after one hour were then counted with the following results:

Calculate the probability that a fly dies when sprayed.            04

(b) Three balls are down from a bag containing 5 white and 3 red balls. If r.v. x denoted the number of white balls drawn from the bag. Then find (i) The probability distribution of x (ii) P(x  2).