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 prepaying 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 preloaded 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 prepay 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:

No. of fitness Classes	Probablity	E(x)
0	0.3	0
1	0.05	0.05
2	0.05	0.1
3	0.05	0.15
4	0.1	0.4
5	0.1	0.5
6	0.1	0.6
7	0.05	0.35
8	0.05	0.4
9	0.05	0.45
10	0.1	1

Suppose Dorothee decides to pre-pay for 7 classes. How many unused credits can she expect to have at the end of the month (prior to receiving a refund)?