H3 Due Oct 7

H3 Due Oct 7 - loan? 1 C) Compare and explain your answers...

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NEW YORK UNIVERSITY DEPARTMENT OF ECONOMICS ECON-UB.18.011: Statistics, Fall 2011 HOMEWORK 3 DUE FRIDAY OCTOBER 7 2011. PLEASE HAND IN THE CLASSROOM AT THE BEGINNING OF CLASS Problem 1 Consider an experiment involving three tosses of a fair coin. De f ne a random variable X=number of heads in three tosses. A) Construct the probability distribution of X. B) Suppose that you know that at least one coin turned up a head. What is the probability that exactly three coins turned up heads? Problem 2 4.20/184 Problem 3 Applet Exercise 4.3/196 Problem Suppose that US Senate is considering the tax cut. A) Suppose that 40 percent of Senators support the tax cut. If 20 Senators are selected at random, what is the probability that 8 will support the loan? B) Suppose that 60 percent of Senators support the tax cut. If 20 Senators are selected at random, what is the probability that 12 will support the
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Unformatted text preview: loan? 1 C) Compare and explain your answers to A) and B). Problem 4 Consider two randomly selected corporate bonds: A and B. Suppose that the probability that bond A defaults is 0.5. If bond A defaults, the probability that bond B defaults is 0.75, whereas if bond A does not default then the probability that bond B defaults is 0.25. A) What is the probability that bond B will default? B) What is the probability that both bonds will default? C) Let Y be the number of bonds that default. Is Y a binomial random variable? D) What is the probability distribution of Y? Hint: List events that correspond to each possible value of Y and then use the conditional probabilities given in the problem to compute that prob-abilities that Y will take each of these values. 2...
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H3 Due Oct 7 - loan? 1 C) Compare and explain your answers...

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