A company has installed 10,000 electric lamps in a metro. If these lamps have an average life of 1,000 burning hours with a S.D. of 200 hours. Assuming normality, what number of lamps might be expected to fail. 

i)  in the first 800 burning hours. 

ii) between 800 and 1200 burning hours.        

iii) more than 1000 burning hours  

The daily consumption of milk in a city, in excess of 20,000 litres, is approximately distributed as a gamma variate with parameters r = 2 and λ = 1/10,000. The city has a daily stock of 30,000 litres. What is the probability that the stock is insufficient on a particular day?

State whether the following statements are True or False and also give the reason in support of your answer.

(a) If odds in favour of an event A are 2:5 then probability of happening of the event A will be .

(b) If two independent events A and B are such that A and B are independent. P(A) = and P(B) =  , then events A and are independent.

c) If X is a discrete random variable with probability mass function (pmf)

The probability that a person living in a certain city owns a dog is estimated to be 0.3. Find the probability that the tenth person randomly interviewed in that city is the fifth one to own a dog.

The distribution function F of a continuous variable is given by

F(x) = 0, if x < 0

= x 2 , if 0 < x < 1

= 1, if x > 3

(i) Find the pdf of X,

(ii) Evaluate P[|X| <1/ 2], using distribution function F,

(iii) Evaluate P[|X| < 1/ 2], using pdf.

 A bag contains 5 balls which are numbered from 1 to 5. Two balls are drawn without replacement from this. Find the expectation of the sum of the numbers on these balls.

A taxi cab company has 12 Ambassadors and 8 Fiats. If 5 of these taxi cabs are in the workshop for repair and an Ambassador is as likely to be in for repair as a Fiat, what is the probability that (i) 3 of them are Ambassadors and 2 are Fiats, (ii) at least 3 of them are Ambassadors, and (iii) all 5 are of the same make?