First Year Second Semester Master In Computer Application Examination

First Year Second Semester Master In Computer Application Examination

(New Course)

Paper – V 2 CSA 5

STATISTICAL AND NUMERICAL MATHEMATICS

Time : Three Hours ] [ Max. Marks : 80

Unit – I

1. EITHER

a) Define statistics. Explain the scope of statistics.
b) Explain the measures of central tendency with an example.

OR

c) Explain census and sampling in detail.
d) Give the relationship amongst different averages.


Unit – II

2. EITHER

a) Explain skew ness and kurtosis with the help of neat diagrams.
b) Explain the measures of dispersion with examples.

OR
c) Define regression. State the properties of regression coefficients.
d) Calculate mean and standard deviation for the following distribution :-



x 2.5-7.5 7.5-12.5 12.5-17.5 17.5.-22.5 22.5-27.5 27.32-32.5
y 12 28 65 121 175 198
x 32.5-37.5 37.5-42.5 42.5-47.5 47.5-52.5 52.5-57.5 57.5-62.5
f 176 120 66 27 9 3


UNIT – III

3. EITHER

a) Explain conditional probability in detail with two examples.

b) State and prove Bayes Theorem.

OR
c) Define classical and statistical probability. Explain the axiomatic approach to
probability.

e) The chances that doctor A will diagnose a disease X correctly is 60%. The chances that a patient will die by his treatment after correct diagnosis is 40% and the chance of death by wrong diagnosis is 70%. A patient of doctor A, who had disease was diagnosed correctly ?


UNIT - IV

4. EITHER

a) Define random variable and probability distribution function. State the properties
of distribution function.

b) Given the following table :-
x -3 -2 -1 0 1 2 3
p(x) 0.05 0.10 0.30 0 0.30 0.15 0.10


Find E(x), E(4x + 5), E(x²), V(x).

OR

c) Define Mathematical Expectation. Derive the addition and multiplication theorem
of expectation.

c) The following is the distribution function of discrete random variable x :-
x -3 -1 0 1 2 3 5 8
f(x) 0.10 0.30 0.45 0.5 0.75 0.90 0.95 1.00

i) Find the probability distribution function of x.
ii) Find p(x is even) and p( I = x = 8 ).
iii) Find p( x = -3 ¦ x < 0 ) and
iv) P ( x = 3¦ x > 0 ).


UNIT – V

4. EITHER

a) Derive the first four moments of binomial distributions.
b) Define geometric distribution. Find it’s mean and variance.

OR

c) Explain Poisson distribution, find its mode.
d) Write a note on normal distribution. Derive the mode and median of Normal distribution.