QUESTION ONE.
(a) The probability that, a bomber sets a target on a bombing mission is 0.70 Three bombers are sent to bomb a particular target.
(i) What is the probability that they all hit the target?
(ii) What is the probability that at least one hits the given target?
(b) Given that the events A, B, and Care mutually exclusive and exhaustive. If P(C) =2P (A) and P(B)=P(A ?C). Determine the probabilities of events A, B and C respectively.
QUESTION TWO.
In an investigation to calculate the relationship between the performance of students in mid-semester examination (X) and end of semester examination (y), the subsequent marks were taken from the records of ten (10) students.
|
X
|
34
|
73
|
96
|
84
|
45
|
63
|
14
|
42
|
83
|
96
|
|
Y
|
43
|
67
|
83
|
80
|
54
|
63
|
24
|
67
|
73
|
90
|
(i) show a scatter plot of the above data
(ii) Fit on your scatter plot the line of best fit
(iii) Evaluate the linear regression function of Y on X
QUESTION THREE.
Use the data given in the table below to determine the following indices:-
|
|
2010
|
2011
|
|
|
Commodity
|
Price
|
Quantity
|
Price
|
Quantity
|
Weight
|
|
A
|
10
|
100
|
12
|
180
|
60
|
|
B
|
12
|
240
|
15
|
450
|
50
|
|
C
|
15
|
225
|
17
|
340
|
30
|
Take 2010 = 100
(i) Laspeyre's price index
(ii) Paasche's price index
(iii) Fisher's ideal index
(iv) Relative price index for commodity A
(v) Weight aggregative price index