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Suppose that you are offered the following "deal." You roll a die. If you roll a six, you win $10. If you roll a four or five, you win $6. If you roll a one, two, or three, you pay $4. 0 Part (a) Part (b] In words, define the Random Variable X. the probability of roling a four O the amount of numbers that can be rolled the amount of winnings the amount of money made by rolling a six X Incorrect. The probability of rolling a four is a fixed value of 1/6. o Part (c) - Part (d) Construct a PDF. (Enter your answers for P(X = x) as fractions. Round your answers for x . P(X = x) to two decimal places) X P(X = x) x . P(X = x) 6 10 4 or 5 1, 2, or 3 Part (e) Over the long run of playing this game, what are your expected average winnings per game? (Round your answer to two decimal places.) SSuppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities, Let X = the number of children married people have. X P(x) XP(x) 0 0.10 0.20 2 0.30 3 0.10 0.05 6 (or more) 0.05 (a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.) (b) In words, what does the expected value in this example represent? the number of children adults in the country have the average number of children married adults in the country have the number of children married adults in the country have the average number of children adults in the country have (c) Find the expected value. (Enter your answer to two decimal place.) children (d) Is it more likely that a married adult will have two to three children or four to six children? How do you know? It is more likely to have four to six children, with p = 0.2 O it is more likely to have two to three children, with p = 0.5 O it is more likely to have four to six children, with p = 0.8 it is more likely to have two to three children, with p = 0.3 it is more likely to have four to six children, with p = 0.1 Activate Win X Go to Settings to