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Winter 2015
PROGRAM- MCA(REVISED FALL 2012)
SEMESTER- FOURTH
SUBJECT CODE & NAME- MCA4020- PROBABILITY AND
STATISTICS
Q1. Three
machines A, B and C produce respectively 60%, 30% and 10% of the total number of items of a factory. The percentage of
defective output of these machines are respectively 2%, 3% and 4%. An item is
selected at random and is found to be defective. Find the probability that the
item was produced by machine C.
Solution: Let P(A), P(B) and P(C) denote the
probabilities of choosing an item produced by A, B, C respectively.
Also, let P(X/A), P(X/B), P(X/C) denote the
Q3. The data shows the
distribution of weight of students of 1st standard of a school. Find
the quartiles.
|
Class Interval
|
13 - 18
|
18 - 20
|
20 - 21
|
21 – 22
|
22 - 23
|
23 - 25
|
25 – 30
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Frequency
|
22
|
27
|
51
|
42
|
32
|
|
16
|
10
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
.
Q4. Fit a trend line to the
following data by the freehand method:
|
Year
|
Production of wheat
|
Year
|
Production of wheat
|
|
|
(in tonnes)
|
|
(in tonnes)
|
|
|
|
|
|
|
1995
|
20
|
2000
|
25
|
|
|
|
|
|
|
1996
|
22
|
2001
|
23
|
|
|
|
|
|
|
1997
|
24
|
2002
|
26
|
|
|
|
|
|
|
1998
|
21
|
2003
|
25
|
|
|
|
|
|
|
1999
|
23
|
2004
|
24
|
|
|
|
|
|
Solution:
Graphical
representation of trend line relating to the production of wheat by the
method of free hand curve is shown in figure
Q5. Let X be a random variable and its
probability mass function is 
find the m.g.f. of
X and hence its mean and variance.
find the m.g.f. of
X and hence its mean and variance.
Solution: By definition,
Q6.
The
diastolic blood pressures of men are distributed as shown in table. Find
the standard deviation and variance.
|
Pressure(men)
|
78-80
|
80-82
|
82-84
|
84-86
|
86-88
|
88-90
|
|
|
|
|
|
|
|
|
|
No. of
Men
|
3
|
15
|
26
|
23
|
9
|
4
|
|
|
|
|
|
|
|
|
Solution:
The table
represents the frequency distribution of data required for calculating
the standard deviation.
|
Class
|
Mid
|
Frequency
|
x-83
|
d = (x-
|
d²
|
fd
|
fd2
|
|
Interval
|
value
X
|
‘f’
|
|
83)/2
|
|
|
|
|
|
|
|
|
|
|
|
|
|
78-80
|
79
|
3
|
-4
|
-2
|
4
|
-6
|
12
|
|
|
|
|
|
|
|
|
|
|
80-82
|
81
|
15
|
-2
|
-1
|
1
|
-15
|
15
|
|
|
|
|
|
|
|
|
|
|
82-84
|
83
|
26
|
0
|
0
|
0
|
0
|
0
|
|
|
|
|
|
|
|
|
|
|
84-86
|
85
|
23
|
2
|
1
|
1
|
23
|
23
|
|
|
|
|
|
|
|
|
|
|
86-88
|
87
|
9
|
4
|
2
|
4
|
18
|
36
|
|
|
|
|
|
|
|
|
|
|
88-90
|
89
|
4
|
6
|
3
|
9
|
12
|
36
|
|
|
|
|
|
|
|
|
|
|
|
|
80
|
|
|
|
32
|
122
|
|
|
|
|
|
|
|
|
|
Get fully solved assignment. Buy online from website
online store
or
plz drop a mail with your sub code
we will revert you within 2-3 hour or immediate
Charges rs 125/subject and rs 500/semester only.
if urgent then call us on 08791490301, 08273413412
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