Download stats assignment 114 and more Assignments Economics in PDF only on Docsity! 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 X have an exponential distribution with mean θ. Show that P (X > x + y |X > x) = P (X > y) 5. Let X be the life in hours of a radio tube. Assume that X is 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 σ can be and still have the purchaser satisfied? 6. Suppose there are total n individuals out of which p individuals support the ban on alcohol and remaining q (> p) oppose it. If we conduct a poll and m (< q) random individuals out of n abstain 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 1
