a) Jane is a coffee connoisseur who enjoys drinking espressos at her local café. On some days she doesn't drink any cups of coffee, and she limits herself to at most 6 cups. Jane decided to record the number of cups of coffee she drank per day over the last year. Let X be the number of cups of coffee that Jane drank on a random day. Based on Jane's records, below is the probability distribution of the number of cups of coffee she drank per day over the last year: Number of cups of coffee (per day) 1 Probability 0.3 ?0.1 0.3 i) Assuming the above probability distribution is proper, find the probability that on a random day Jane had exactly 1 cup(s) of coffee per day. 0.3 (Enter the exact value) ii) Use the above table to calculate the average number of cups of coffee that Jane drank per day. 2.3 (Enter the exact value) iii) Use the above table to calculate the standard deviation of the number of cups of coffee that Jane drank per day. (Enter the numerical part of your answer correct to at least 2 decimal places in the box. For example, if your answer is 3.17873, enter 3.18)