Download JNTUH (Jawaharlal nehru technological university) MCA (Master of Computer Applications) 1st Year (First Year) Regulation-R19 2021 July-August 861AD Computer Oriented Statistical Methods Previous Question Paper
R19
Code No: 861AD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
2021 MCA I Semester Examinations, July/August - 2021
COMPUTER ORIENTED STATISTICAL METHODS
Time: 3 Hours
Max. Marks: 75
Answer any five questions
All questions carry equal marks
- - -
1.a)
In a certain assembly plant, three machines, B1, B2, and B3, make 30%, 45%, and 25%,
respectively, of the products. It is known from past experience that 2%, 3%, and 2% of
the products made by each machine, respectively, are defective. What is the probability
that a randomly selected finished product is defective?
b)
You enter a chess tournament where your probability of winning a game is 0.3 against
half the players 0.4 against a quarter of the players and 0.5 against the remaining quarter
of the players you play a game against a randomly chosen opponent. What is the
probability of winning?
[8+7]
2.a)
A random variable X may assume 4 values with probabilities 1+3 1- 1+2 1-4
,
,
,
.
4
4
4
4
Find the condition on x so that these values represent the probability function of X.
b)
The joint probability density function of two random variables X and Y is
5 2 0 < < < 2
16
, = 0
Find : i) the marginal density of X and Y ii) Are X and Y are independent? [7+8]
3.a)
Find the mean of the random variable whose probability density function is given by
f(x) = 3/5 10-5 (100 ? x) 0 x 100.
b)
If X is the number appearing on a die when it is thrown, show that the Chebshev's
theorem given P[ X - > 2.5] < 0.47, while the actual probability is zero.
[8+7]
4.a)
Show that mean = variance for a Poisson distribution.
b)
Probability of a success is given by 0.4 if n = 8, find the i) P(x1) ii) P(0<x<4) . [7+8]
5.a)
The lognormal distribution is found to be a good model for strains in structural members
caused by wind loads. Let the strain be represented by X, with mX = 1 and variance of X
is 0.09. (i) Determine the probability P(X > 1 2). (ii) If stress Y in a structural member is
related to the strain by Y = a + bX , with b > 0, determine f Y (y) and mY .
b)
The life of a power transmission tower is exponentially distributed, with mean life 25
years. If three towers, operated independently, are being erected at the same time, what is
the probability that at least 2 will still stand after 35 years?
[8+7]
6.a)
Take 30 slips of paper and lable 5 each -4 and +4, lable 4 from each -3 and 3, three each
-2 and 2 and two each -1, 0, and 1. If each slip of paper has the same probability of
2021
being drawn, find the probabilities of getting -4,-3,-2,-1,0,1,2,3,4 and find the mean and
the variance of this distribution.
b)
Find the probabilities that a random variable having the standard normal distribution will
take on a value i) Between 0.87 and 1.28 ii) between -0.34 and 0.62.
[7+8]
7.a)
A manufacturer of electric lamps is testing a new production method that will be
considered acceptable if the lamps produced by this method result in a normal population
with an average life of 2,400 hours and a standard deviation equal to 300. A sample of
100 lamps produced by this method has an average life of 2,320 hours. Can the
hypothesis of validity for the new manufacturing process be accepted with a risk equal to
or less than 5%?
b)
Among 200 items 50 are defective and from another sample among 400 items 80 are
defective. Test at 0.05 level whether there is a significant difference between the
proportions.
[8+7]
8.a)
Find the linear least square fit y = a x + b for the experimental data points given by:
{(1 , 2) , (3 , 4) , (2 , 6) , (4 , 8) , (5 , 12) , (6 , 13) , (7 , 15)}
b) The following regressions equations were obtained from a correction table
y = 0.516x + 33.73
x = 0.512y + 32.52
Find the value of i) The correlation coefficient ii) The mean x's iii) the mean of y's.
[7+8]
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This post was last modified on 16 March 2023