STA301 Assignment No.3 solution Fall 2010 (Total Marks 30)

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Question 1 2+2+6=10Marks

a) Define Bernoulli trail and Binomial Experiment.
b) In which condition, Poisson distribution is used to approximate hypergeometric distribution?
c) Find the probability that (i) No defective bolt (ii) at most 5 defective bolts will be found in a box of 200 bolts if it is known that 2 percent of such bolts are expected to be defective.

Question 2 3+5+2=10Marks
a) If its rain, an umbrella salesman can earn $ 30 per day. If it is fair, he can lose $ 6 per day. What is his expectation if the probability of rain is 0.3?

b) Show that the following is a density function.

f(x) = 0 < x < 2
= 0 elsewhere
c)







Question 3 2+2+6=10Marks
a) From the following table find P(X + Y < 1);



b) Write this expression h (3; 70, 20, 5) in probability notations/function.

c) An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 800 hours and a standard deviation of 40 hours. Find the probability that
(i) A bulb will burn between 778 and 834 hours.
(ii) A bulb will burn in less than 778 hours.
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