B.SC-III 'C'
ASSIGNMENT-1
B.SC-III (Hous)
1.
Define the following
(i)
Classical definition of Probability
(ii)
Mutually exclusive events
(iii)
Conditional Probability
2.
State and prove Multiplication law of probability.
3.
State and prove Baye's theorem.
4.
When are two events said to be independent. If 'A' and 'B' are two
independent events, show that A and B are also independent ?
5.
Define a discrete random variable and probability mass function. For
what value of K is the following function a proper p.m.f ?
X=x :
-2
-1
0
1
2
3
P(X=x):
0.1
K
0.2
2K
0.3
K
Also Calculate E(X) and V(X).
6.
State and prove Addition theorem of expectation.
7.
Define Binomial distribution and discuss its additive property.
8.
Determine the binominal distribution for which mean is 4 and variance
is
9.
4
. Also find P( X  1 ).
3
Define Poisson distribution. What are its application? Find mgf of
Poisson Variate.
10.
Define Normal distribution. State its important properties.
11.
Obtain the points of inflexion for the normal distribution.
12.
Show that for the uniform distribution f  x  
1
;  a  x  a mgf about
2a
1
sin hat.
at
If X and Y are two random variable having joint density function.
 1
 (6  x  y ); 0  x  2; 2  y  4
f ( x, y ) =  8

0, otherwise
origin is
13.
14.
Find (i) P (X < 1  Y <3)
(ii) P (X < 1 Y <3)
Calculate coefficient of correlation of the pair of observation.
(1,3), (2,10), (3,5), (4,1), (5,2), (6,9), (7, 4) (8, 8), (9,7), (10,6)
15.
Six dice are thrown 729 times. How many times do you expect at least
3 dice to show a five or six?