AS 2 SY BBA

AS-2  

•  Assuming that the typing mistake per page committed by a typist follows a Poisson distribution; find the expected frequencies for the following distribution of typing mistakes:

Number of mistake per page	0	1	2	3	4	5
Number of pages	40	30	20	15	10	5

 (e^-1.5 = 0.22313)  

• The following table give the number of days in a 50 days period during which automobile accidents occurred in a city. Fit a poisson distribution to the data (e^-0.9 = 0.4066)

No. of accidents	0	1	2	3	4
No. of days	21	18	7	3	1

•  It is given that 3 per cent of electric bulbs manufactured by a company are defective. Find the probability that a sample of 100 bulbs will contain (i) no defective (ii) exactly one defective.  (e^-3  = 0.05)
•  In a company during a break time of half an hour on average 15 calls are coming. find the probability that (i) there are at least 2 calls per five minutes (ii) There are at the most 2 calls per five minutes.
•  If mean of a Poisson distribution is 4, then find standard deviation of the distribution.
• The minor injuries a cricket player can expect during the net practice is a random variable having the Poission distribution with (Lamda) = 4.4. Find the probability that during the net practice there will be at the most one minor injuries.
• Give properties of Poission distribution.

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.       

BBA First Year : AS 1

Last day of submission : 23/07/2017