Suppose Alana has personal wealth of $10,000 and there is a probability of 0.2 of losing her car worth $6,400 in an accident. Her utility (of wealth) function is given by u(w) = w0.5, where w is wealth. Word limit per question: 400 words (200 words per part of question)

(a) What is Alana's expected wealth, expected utility, and utility of expected wealth? If she can insure "fully", and if this insurance is fair, how much would it cost her?

(b) What is the maximum amount Alana would be prepared to pay for full insurance? What is the certainty equivalent and the risk premium associated with the uncertain situation she is in if she does not have any insurance? What difference would it make if her utility of wealth function were instead u(w) = 5w?

A weighted coin has a probability of 0.6 to land on “tails” and will always land on either “heads” or “tails.” Which of the following statements is false?

We are interested in studying the effects of attending a private high school on the probability of attending college. For concreteness, let college be a binary variable equal to one if a student attends college, and zero otherwise. Let PrivateHS be a binary variable equal to one if the student attends a private high school. A linear probability model is:

college=B₀+B₁PrivateHS+other factors+u

where the other factors include gender, race, family income, and parental education.

(v) Propose an alternative instrument for PrivateHS and discuss whether the two requirements needed are valid.

Four dice are tossed. Find the probability that (a) the sum is 10, (b) the sum is 15, (c) two dice comes up 1 and two dice come up?

Suppose that a signal s that takes on values 1 and -1, with probability p and 1-p respectively, is sent from location A. The signal received at location B is Normally distributed with parameters (s, 2). Find the best estimate of the signal sent, in the Maximum Likelihood Estimate sense, if R, the value received at location B, is equal to r.

The Poisson probability distribution, associated with a waiting line, is characterized by a parameter known as arrival rate. Explain this concept and describe its connections with the management of a waiting line.

Suppose that a signal s that takes on values 1 and -1, with probability p and 1-p respectively, is sent from location A. The signal received at location B is Normally distributed with parameters (s, 2). Find the best estimate of the signal sent, in the Maximum A Posteriori sense, if R, the value received at location B, is equal to r.

The following table shows the probability of default (%) for companies starting with a particular credit rating. Time (years) 1 2 3 4 5 7 10 Aaa 0.000 0.013 0.013 0.037 0.104 0.241 0.489 Aa 0.022 0.068 0.136 0.260 0.410 0.682 1.017 A 0.062 0.199 0.434 0.679 0.958 1.615 2.759 Baa 0.174 0.504 0.906 1.373 1.862 2.872 4.623 Ba 1.110 3.071 5.371 7.839 10.065 13.911 19.323 B 3.904 9.274 14.723 19.509 23.869 31.774 40.560 Caa 15.894 27.003 35.800 42.796 48.828 56.878 66.212 Which of the statements is correct? Choose all that apply. Read here 1. The probability that a bond initially rated Aa will default during the first year is 0.022%. 2. The probability that a bond initially rated Baa will default by the end of the seventh year is 2.872% .... wink wink

1. Amy’s birthday is on December 6. What is the probability that at least one of the 40 students in ST 421/521 has the same birthday as Amy? (Provide a numerical expression, but don’t attempt to simplify. Assume there are 365 days in every year.)

If a z-score is less than -3.49 it will have a probability equal to what?