Statistics for Economics : Assignment 3
1. Suppose the Monetary Policy Committee (MPC) members decide independently on
interest rate and the probability of decision being correct is p. If the majority decision
is final decision, then what should be preferred number of members in the committee:
one member or 3 members in the committee? Is it possible to always get an unique
value for number of members corresponding to the values of p? explain.
2. Let the numbers of fatal car accidents in a certain state obey the Poisson distribution
with the average of one per day.
(a) What is the probability of more than ten such accidents in a week?
(b) What is the probability that more than 2 days will lapse between two such acci-
dents?
3. You have studied the binomial distribution. For the following questions, define the
random variable clearly and then write down the values of n(number of trials) and p
(the probability of success):
(a) If 25% of the balls in a particular urn are red, and if 15 balls are drawn at random
with replacement from the urn, what is the probability that more than four red
balls will be selected?
(b) A healthcare worker wants to understand the prevalence of ART among HIV/AIDS
patients in a city. For this she conducts a survey of HIV/AIDS patients. It is also
known that one out of every four HIV/AIDS patients have received ART. In the
survey there are 100 HIV/AIDS patients. What is the probability that exactly 20
people have received ART? What is the probability that at least 10 people have
received ART?
4. Let Xhave an exponential distribution with mean θ. Show that P(X > x +y|X >
x) = P(X > y )
5. Let Xbe the life in hours of a radio tube. Assume that Xis normally distributed with
mean 20 and standard deviation σ. If a purchaser of such radio tubes requires that at
least 90 percent of the tubes have lives exceeding 150 hours, what is the largest value
σcan be and still have the purchaser satisfied?
6. Suppose there are total nindividuals out of which pindividuals support the ban on
alcohol and remaining q(> p) oppose it. If we conduct a poll and m(< q) random
individuals out of nabstain from voting, then find the probability that a majority of
voters will vote against the alcohol ban?
7. A city has 5000 children. Further, 800 children have not been vaccinated against polio.
65 of the city’s children are enrolled in a preschool. Suppose the municipal health
department sends a doctor and a nurse to the preschool to immunize any child who
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