Inter (Part-I)   
Lahore Board 2012
Statistics   
Paper I (Objective Type)
Time Allowed: 20 Minutes    
Max. Marks: 17

Note: Four possible answers A, B, C and D to-each question are given. The choice which you think is correct, fill that circle in front, of that question with Marker or Pen ink. Cutting or
filling two or more circles will result in zero mark in that question. Write the letter A, B, C or D in the column (write correct option) against each question also. If there is contradiction in the bubble and hand written answer, bubble option will be considered correct,

Q1.

• If the Mean=40,  Mode = 42, the distribution is :
  

(A) Symmetrical
(B) +vely skewed
(C) vely skewed
(D)  None of these

• If X and Y are two independent variable then E (XY)
  

(A) E(X) + E(Y)        
(B) E(X).E(Y)
(C) E (X) –E (Y)
(D) Zero

• Standard deviation of 3, 3, 3, 3, 3 is equal to
  

(A) 8              
(B) 3               
(C) Zero                     
(D) 16

• The number of permutation for `1.1 objects taken out of total ‘n' objects is
  

(A) NCn             
(B) n Cs           
(C) n Pr            
(D) n Cr

• Colour of hair is a
  

(A) Continuous variable
(B) Discrete variable
(C) Qualitative variable
(D) Quantitative variable       

• If all the values consider equal importance in index  is :

(A) Simple     
(B) Weighted             
(C) Unweighted         
(D) None of these

• Mean of binomial distribution is :

(A) Npq        
(B) xp                        
(C) np                         
(D) √npq                           

• An expected value of a random variable is equal to its:
  

(A) Variance  
(B) Mean                    
(C) S.D.                      
(D) None of these

• The hypergeometric distribution has parameters
  

(A) 2             
(B) 3                           
(C) 4                           
(D) None of these

• It An ogive is a

(A) Frequency polygon
(B) Frequency curve
(C) Cumulative frequency
(D) None of these

• First moment about mean is equal to:
  

(A) One          
(B) 3                           
(C) Zero                     
(D) All of these

• In a binomial experiment, the successive trials arc
  

(A) Independent       
(B) Fixed        
(C) Dependent           
(D) Mutually

• The index number given by   x100 is:
  

(A) Laspeyre’s index  
(B) Value index 
(C) Paasche's index
(D) None of these

• The probability of sure event is
  

(A) Negative             
(B) Zero         
(C) One                      
(D) None of these

• The sum or deviation from mean is
  

(A) 5              
(B) Zero                     
(C) 3                           
(D) l

• The difference between largest and smallest value is
  

(A) Interval  
(B) S.D.                      
(C) Range                   
(D) None of these

• What is total angle of pie diagram
  

(A) 90°           
(B) 180°                    
(C) 360°                    
(D) None of these

SECTION-I
SUBJECTIVE TYPE

2. Write short answers to any EIGHT (8) questions:    

• Differentiate between continuous and discrete variable.
  
• What is primary data?
  
• Wit is weighted arithmetic mean?
  
• Rime some disadvantages °rifle made_
  
• The sum of deviation of 10 values from 15 is 20. Find Aramaic mean.
  
• If Mean = 20 , Median -= 18.67, find &lode?
  
• Find GAL if X= 1, 3, 9
  
• Define index number.
  
• Write the name of dome different types of index number.          
  
• If Laspeyre’s index no. is 180 and Fisher's Index no is 120, find Paasche's Index number.
  
• Explain the selection of the suitable average in W.P.1.
  
• Given  = 120 , =1210 Find Paasche’s  Price Index number.

3. Write short answers to any EIGHT (8) questions:       

• Differentiate between classification and tabulation.
• How a frequency polygon is constructed?
• Given  = 120, - 296 and mode = 2.944,comnent on the skewness.
• X of 200 items is 48 and their S2 is 9. Find of .
• Define Inter Quartile Range and Quartile Deviation.
• Define coefficient of variation. What arc uses?
• Define the moment ratios β1 and β 2. For what purposes these are computed?
• Draw the shapes of meso-kurtic, platy-kurtic and lepto kurtic curves.
• Write the empirical definition of probability.
• Define equally likely events and exhaustive events.
• Write the sample space when 3 coins are tossed.
• Given P (A) = 0.6 ; P (8) 0.5, P(A∪B)= 0.9, then find P(A∩B)=?

4. Write short answers to any SIX (6) questions:      

• Find E (5- 3y) , when E (y) = 1.4
• Check for y = 1, 2, 3,4. Is f(y)=  a p.d.f ?
• Define continuous random variable.
• How do we generate random variable?
• What is mathematical expectation of constant?
• What is Bernoulli trail?
• Write the parameters of hypergeometric distribution.
• If X is a binomial random variable, find P (X - 3) when n = 3 and P
• What is mean, variance and S.D. of (q + p)4 ?

(SECTION - II)

Note: Attempt any THREE questions.

5.
(a) Calculate Harmonic Mean of the data given below       

(b) Calculate Mode and P40 of the data given above.        

6.
(a) Calculate coefficient of variation.

If n= 150        

(b) The first three moments of a distribution about the value are , 8 and 20.
Find     (i) Variance,    (ii) is the distribution positively skewed or negatively skewed.

7.
(a) Compute the Fisher's ideal Price Index Number for the year 2001 taking 2000 as base year.

(b)  A bag contains 4 red and 6 green balls out of which 3 are drawn. Find the probability of drawing:
(i) 2 red and one green ball.           
(ii) All red balls.

8.
(a) The probability distribution of a r.v. 'x' is given by :
F(x)=3 Cx  3-x               x=0,1,2,3
Find Mean and Variance of distribution.

(b) A continuous random variable 'X' has p.d.f; f(x) =2x 0 ≤ x ≤ 1
Find 
(i) P(x) =                     
(ii) P

9.
(a) In a binomial distribution n = 5. What is the value of other parameters of P (X= 0 ) = P
( X= 1), Find the mean of the distribution.

(b) Three balls are drawn from a bag contains 5 white and 3 black balls, if X denotes the number of white halls drawn from the bag, then find the probability distribution of X?
Also find out mean and variance.