e basics tion 6.1 Introduction to Random Variables and Probability Distributions 6. | Statistical Literacy Consider the probability distribution of a random variable x. Is the expected value of the distribution necessarily one of the possible values of x? Explain or give an example. 7.| Basic Computation: Expected Value and Standard Deviation Consider the probability distribution shown in Problem 3(a). Compute the expected value and the standard deviation of the distribution. 8.| Basic Computation: Expected Value For a fundraiser, 1000 raffle tickets are sold, and the winner is chosen at random. There is only one prize, $500 i> cash. You buy one ticket. (a) What is the probability you will win the prize of $500? (b) Your expected earnings can be found by multiplying the value of the prize by the probability you will win the prize. What are your expected earnings? (c) Interpretation If a ticket costs $2, what is the difference between your "costs" and "expected earnings"? How much are you effectively contrib- uting to the fundraiser? I Cuitigal Thinking: Simulation We can use the random-number table to Jose Sur parther support page for a guide on the basics. () (d) Weight of a football player chosen at random (e) Number of lightning strikes in Rocky Mountain National Park given day 3. Statistical Literacy Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer. (a) 1 (b) 0. 1 P(x) 0.25 0.60 0.15 P(x) 0.25 0.60 0.20 4.| Statistical Literacy At State College all classes start on the hour, with the ear- liest start time at 7 A.M. and the latest at 8 P.M. A random sample of freshmen showed the percentages preferring the listed start times. Start Time 7 or 8 A.M. 9,10,or 11A.M. 12or 1 P.M. 1P.M., or later after 5 P.M., % preferring 10% 35% 28% 25% 15% Can this information be used to make a discrete probability distribution? Explain. 5. | Statistical Literacy Consider two discrete probability distributions with the same sample space and the same expected value. Are the standard deviations of the two distributions necessarily equal? Explain. 2.