Eight coins are tossed together and the occurrence of a head is termed a success. Write down the Binomial distribution of probabilities for the occurrence of 0, 1, 2....8 heads. What is the arithmetic mean and what is the variance of this distribution?
A.  2 
B.  9 
C.  3 
D.  5 
Option: A Explanation : P = 1/2, q = 1/2, n = 8 Mean = np = 8 x 1/2 = 4 Variance (σ)^{2} = npq or 8 x 1/2 x 1/2 = 2 
Given
Mean Standard deviation 
X series 
Y series 
18 
100 

14 
40 
Coefficient of correlation between X and Y series = +0.8.
Find the most probable value of Y if X is 70 and most probable value of X if Y is 90
A.  130.12 
B.  159.30 
C.  159.48 
D.  130.36 
Option: C Explanation : The find out value of X when Y = 90
To find out the value of Y when X = 70
Hence the answer is (c). 
What is the probability of getting all the heads in four throws of a coin?
A.  1/13 
B.  12/16 
C.  11/16 
D.  1/16 
Option: D Explanation : The chance of getting head in the first throw = 1/2 The chance of getting head in the second throw = 1/2 The chance of getting head in the third throw = 1/2 The chance of getting head in the fourth throw = 1/2 Thus the probability of getting heads in all the throws = (1/2) x (1/2) x (1/2) x (1/2) = 1/16 Hence the answer is (d). 