Read the (same as for the previous questions). Suppose Dorothee decides to pre-pay for 7 classes. How many extra classes can she expect to have purchased at the $12 price by the end of the month? Read the problem description here (same as for the previous questions). Suppose Down Dog Yoga proposes a different payment scheme: customers can sign into the warrior program which gives them the possibility of paying $8 per class as they come into the fitness center with no-prepaying required. Enrolling in this program costs $20 per month. Calculate Dorothee's expected cost for fitness classes in May if she chooses this payment scheme. Read the problem description here (same as for the previous questions). Suppose Dorothee decides to pre-pay for 7 classes. What is her expected cost for fitness classes over the coming month? Read the problem description here (same as for the previous question). Suppose Dorothee decides to pre-pay for 7 classes but attends 9 classes during the month. How much is her total cost for fitness classes over the month? Read the problem description here (same as for the previous questions). Suppose Dorothee decides to pre-pay for 5 classes. With what probability will she run out of credits? Read the problem description here (same as for the previous questions). Suppose Dorothee decides to pre-pay for 7 classes. What proportion of the classes she will attend can she expect to have been pre-paid for (i.e., fill rate)? Read the problem description here (same as for the previous questions). How much would Dorothee expect to spend on fitness classes in May if she could see the future, that is, if she could accurately predict how many classes she will attend over the month of May? .any classes should Dorothee pre-pay for on May 1st if she wishes to minimize her expected cost for fitness classes over the month of May? Hint: to answer this question you must calculate the overage cost, the underage cost and the critical fractile. Make sure you include these in your answer. Read the problem description here (same as for the previous question). Suppose Dorothee decides to pre-pay for 7 classes but only attends 2 classes during the month. How much is her total cost for fitness classes over the month? Read the problem description here What is the expected number of fitness classes which Dorothee will be able to attend over the coming month? Down Dog Yoga is a fitness studio which offers a variety of fitness classes such as yoga, Pilates and Barre. On the first day of each month, customers have the option of pre-paying for classes at a discounted rate of $8 per class. The purchased classes are loaded onto a smartphone app. Upon entering the studio to take a class, the customers scan their phone to use up one of the class credits pre-loaded on their app. If they come in for a class and have run out of credits on their app, they can purchase access to a class for a price of $12 per class. If, on the other hand, they reach the end of the month and still have some class credits, they receive a refund for $2 per class credit remaining. The credit balance is then reset to zero on the first day of each month for each customer. On May 1st, Dorothee is trying to decide how many classes she wants to pre-pay for. Based on past observations and her schedule for the month, she estimates she will be able to attend between 0 and 10 classes over the course of the month, with the following table giving the corresponding probability for each value