The following figure shows probability distributions, namely, Expont and Expon2, of inter-arrival phone calls at two different call centers. Note that the inter-arrival times in each call center are exponentially distributed, with rates Lambda1 and Lambda2, respectively. Expon(1) Expon(2) Based on the figure, which statement is true? Lambda 1 > Lambda 2 Lambda 2 > Lambda 1 Lambda 1= Lambda 2 O Not enough information

A commuter must pass through three traffic lights on her way to work. For each traffic light, the probability that it is green when she arrives is 0.6. The lights are independent. 3 (a) Compute the probability that all three lights are green. (b) The commuter goes to work five days per week. Let X be the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another. Determine the distribution of X. (c) Calculate P(X= 3).

1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.

In the sport of basketball, a player will sometimes get the opportunity to shoot two free throws without being affected by any other players in the game.  Assume that, for one player, these two free throws are independent of each other.  If this player makes free throws 80% of the time, what is the probability that this player will make neither free throw in the opportunity?