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# Ma6453 Important questions PROBABILITY AND QUEUEING THEORY

## Sample Ma6453 Important questions:

1. Find the mean and variance of the following distributions:
Binomial, Poisson( Refer B: page no:179,183)

2. Find the mean and variance of the following distributions :
Geometric and Exponential(Refer B : page no:185,212)

3. Prove that Poisson distribution is the limiting form of
Binomial distribution. (Refer B: page no : 181)

4. Each of the 6 tubes of a radio set has a life length (in yrs) which may be considered as a RV that follows a weibull distribution with parameters α = 25 and β = 2. If these tubes function independently of one another, what is the probability that no tube will have to be replaced during the first 2 months of service? (Refer C: page no : 2.82)

5.It is known that the probability of an item produced by a certain
machine will be defective is 0.05. If the produced items are sent to the market in packets of 20, fine the no. of packets containing at least, exactly and atmost 2 defective items in a consignment of 1000 packets using (i) Binomial distribution (ii) Poisson approximation to binomial distribution. (Refer C: page no : 2.28)

6. The daily consumption of milk in excess of 20,000 gallons is
approximately exponentially distributed with θ = 3000. The city has a
daily stock of 35,000 gallons. What is the probability that of two days
selected at random, the stock is insufficient for both days.
(Refer C: page no : 2.74)

 Subject Name PROBABILITY AND QUEUEING THEORY Subject code MA6453 Regulation 2013