Rashtrasant Tukadoji Maharaj Nagpur University 2007-2nd Year M.C.A First Semester Master In Computer Application - Question Paper

First Year 2nd Semester Master In Computer Application exam

(New Course)

Paper – V two CSA 5

STATISTICAL AND NUMERICAL MATHEMATICS

Time : 3 Hours ] [ Max. Marks : 80

Unit – I

1. EITHER

a) Define statistics. discuss 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 various 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 subsequent 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) discuss conditional probability in detail with 2 examples.

b) State and prove Bayes Theorem.

OR
c) describe classical and statistical probability. discuss 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 accurate 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 subsequent table :-
x -3 -2 -1 0 1 2 3
p(x) 0.05 0.10 0.30 0 0.30 0.15 0.10


obtain E(x), E(4x + 5), E(x²), V(x).

OR

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

c) The subsequent 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 = eight ).
iii) Find p( x = -3 ¦ x < 0 ) and
iv) P ( x = 3¦ x > 0 ).


UNIT – V

4. EITHER

a) Derive the 1st 4 moments of binomial distributions.
b) Define geometric distribution. obtain it’s mean and variance.

OR

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

Earning:   Approval pending.