Kerala Class 12 First Term Question Paper 2023 Statistics

Kerala Board

First Term
Question Paper

HIGHER SECONDARY FIRST TERMINAL EXAMINATION AUGUST 2023
STATISTICS - HSE II
—-------------------------------------------------------------------------------------------------------------------
Time 2 hours (Cool Off Time: 15 minutes) Maximum mark 60

Answer any 8 questions from 1 to 9. Each question carries 2 scores.

1. (i) The point of intersection of two regression lines is..................
...................

(ii) The equation of regression line of X on Y is 3x + 2y - 5 = 0 then =
X on Y is 3x + 2y - 5 = 0

(a) (b) (c) (4)

2 Classify the correlation in the following pairs of variables into positive, negative and zero.
?

(i) Time and Speed (ii) Height and Weight
(iii) Beauty and Intelligence (iv) Shoe size and Intelligence
3. The probability distribution of a random variable X is:. f(x) = kx ; 0
Find the value of k.
X

f(x) = kx ; 0 .

k .

4. Find if y =4

y =4

5. In a regression analysis, the following results were obtained.
=0.6, Standard Deviation of Y = 5.48 r = 0.83. Find Standard Deviation of X.
=0.6, SD of Y = 5.48 r = 0.83 . y

6. The total revenue function of a firm is given by R(x) = where 'x' is the number of units sold.
Find the marginal revenue function.

total revenue function R(x) = .

7. A coin is tossed 4 times. What is the probability of getting exactly 3 heads?
?

8. A random variable X has the following probability distribution. Find E(X).
E(X)

X -1 0 2

P(x) 0.3 0.2 0.5

9. Match the following ( )

A B

(i) No correlation (a) Rank correlation coefficient

(ii) (b) r=

(iii) (c.) Correlation coefficient
1-

(iv) Perfect correlation (d) r=0

Answer any 6 questions from 10 to 16. Each question carries 3 Score.
10. A curve is represented by the equation f(x) = Find the area bounded by the curve in between X
axis, and the lines x = 1 and x = 3.
f(x) = . ഈ

X axis, x = 1, x = 3 .

11. In a statistical analysis of 10 observations on Price(X) and Supply(Y), the following data were obtained.
Price(X), Supply(Y) 10

.

x = 140 y = 230 , =1.02. = 0.91
(i) Obtain the equation of regression line of Y on X.
Y on X
(ii) Estimate the supply, when the price is 15 units.
15

12. (a) Choose the correct answer. If ∫ , then the value of ‘n’ is

If ∫ n

(1) 10 (ii) 9 (iii) - 10 (iv) - 9

(b) In a factory the cost of manufacturing 'x' units is given by c(x) =
Find the minimum cost.
c(x) =
, ?

13. The following data relate to the height of father (X) and that of son (Y); Calculate Karl Pearson's
Correlation Coefficient.

.

n = 7, xy= 31917, =31451, =32402, x=469 y = 476
14. The average number of deaths due to snake bites (X) in a village in a year is 2.
(X) 2 .

(a) Identify the distribution of X.
X

(b) Write the p.d.f. of the distribution.
X pdf

(c) What is the probability that the number of deaths due to snake bite in a year is one?
?

15. Random variable X has the following density function.
.

( ) ( ) : x=0,1,2,...,5

Find (a) Values of the parameters of the distribution.

(b) Mean and variance of the distribution.

16. For a Poisson variable X. P(X = 1) = P(X = 2)
P(X = 1) = P(X = 2)

(a) Find the mean of X. a)

(b) Calculate P(X < I) b) P(X < I) (6 * 3 = 18)

Answer any 4 questions from 17 to 21. Each question carries 4 scores.
17. A continuous random variable X has the probability function, f(x) = 2x;
Find (a) E(X) (b) E(1 - 2X)

18. The price (X) and demand (Y) have the two regression equations.
The price (X), demand (Y)
2x - 5y + 11 = 0 and 8x - 9y - 22 = 0
Find (a) The correlation coefficient ( )

(b) The average price and average demand ( price demand )

19. (a) Draw a scatter diagram for the following data
.

X : 10 22 34 35 69 85 95 98
Y : 32 36 25 45 32 56 86 68

(b) If = 26.7 , = 508.4 = 4.6 = 36.8 r = 0.52 .

Find the regression equation of X on Y. (X on Y )

20. (a) ; f(x) is……
(i) Discrete probability function (ii) Continuous probability function.
(iii) Discrete random variable (iv) Continuous random variable
(b) Let X be the number of defective items when 2 items are shipped and P(x) be the probability of
x defective items. Use the table below to find P(X = 2)
X

. X . P(X = 2)

X 0 1 2

P(x) -

21. (a) If F(x) is the cumulative density function of a continuous random variable X then F(- ) = ....
F(x) X cdf . F(- ) = ....

(b) Examine whether can be a p.d.f.
(4 * 4 = 16)

Answer any 2 questions from 22 to 24. Each question carries 5 Score.
22. (i) Find
(a) (b) (c.) (d)

(ii) Find the value of 'c' if ∫

∫ c ?

23. The scores obtained by 12 students in a written test and ranks in performance are given below. Find
rank correlation coefficient.
12

.

Scores in written test 12 15 18 20 18 16 13 18 17 11 13 18

Rank in Performance 8 7 2 1 6 5 11 4 9 12 10 3

24. A random variable X has the following probability distribution.

X 0 1 2 3 4 5 6 7

P(X) a 4a 3a 7a 8a 12a 6a 7a

(a) Find the value of 'a' (a )

` (b) Find
(i) P(X < 3) (ii) P(X 4) (iii) P(0 < X < 5) ( )

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