SY BBA QM III : AS-1

AS-1

1. The probability distribution of a random variable x is given below. Find E(x) and V(x).

   X	-2	-1	0	1	2
   P(x)	2k	K	3k	3k	k

2.  The following table show the distribution of 128 samples. Fit a binomial distribution and find expected frequency:

X	0	1	2	3	4	5	6	7
Samples	7	6	19	35	30	23	7	1

2.                 

                        3. The probability function of binomial distribution is P(x) = 10Cx (0.8)^x (0.2)^(10-x), then find its variance.

3.       The probability distribution of a random variable  x  is as follow: Find mean and S.D.

Xi	2	3	4	5	6	7	8	9	10
P(Xi)	0.05	0.1	0.3	0.2	0.05	0.1	0.05	0.1	0.05

4.       

                4. The probability distribution of a random variable x is given below, find mean and variance.

X	8	12	16	20	24
P(X)	1/8	1/6	3/8	1/4	1/12

5.       

                         5.    Four coins are tossed simultaneously. find the probability of getting 2 head.

6.       

                6.   A and B play a game in which the probability of winning of A is 2/3, find the probability that A will win at least 6 times out of 8 trials.

               7.  The probability that in certain correspondence course student will graduate is 0.4. Determine the probability that out of 5 students (a)none (b) one (c) at least one will graduate.