Practice Questions: 1. An 8 sided die is rolled with each outcome equally likely. Let x be the random variable that records the outcome from the sample space: {1, 2, 3, 4, 5, 6, 7, 8}. a. What is the mean of x? b. What is the standard deviation of x? 2. One time while playing a video poker game, I bet $1 and was lucky enough to receive a hand in which I could draw to an open ended straight flush. If I made a straight, I would win $4. If I made a flush, I would win $6. If I made a straight flush, I would win $50. In all other cases, I would lose $1. Note: The events of making a straight, flush, and straight flush are mutually exclusive. What is my mathematical expectation in this situation? Discuss the significance of this answer being positive, negative, or zero. Straight Flush Straight All Other Flush Outcomes Amount Won (Profit) $4 $6 $50 -$1 Probability of Making 6 7 2 32 Hand 47 47 47 47