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 $5.Part (a)What are you ultimately interested in here (the value of the roll or the money you win)?the number rolledthe type of die the number of times a six is rolledthe number of winningsPart (b)In words, define the Random Variable X.the probability of rolling a fourthe amount of money made by rolling a sixthe number of winningsthe number of numbers that can be rolledPart (c)List the values that X may take on. a.1, 2, 3, 4, 5, 6b.4, 5, 6 c. $5, $6, $10 d.−$5, $6, $10Part (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.) XP(X = x)x · P(X = x)6 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.)=Part (f)Based on numerical values, should you take the deal? Yes, you should take the deal because the expected value is positive.No, you should not take the deal because the expected value is negative.

Part (a) The ultimate interest in this scenario is the money you win. Part (b) Random variable X can…

Answered: Suppose that you are offered the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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 $5.

Part (a)

What are you ultimately interested in here (the value of the roll or the money you win)?

the number rolled
the type of die
the number of times a six is rolled

the number of winnings
Part (b)

In words, define the Random Variable X.

the probability of rolling a four

the amount of money made by rolling a six

the number of winnings

the number of numbers that can be rolled

Part (c)
List the values that X may take on.

a.1, 2, 3, 4, 5, 6

b.4, 5, 6

c. $5, $6, $10

d.−$5, $6, $10
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

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.)

=
Part (f)

Based on numerical values, should you take the deal?

Yes, you should take the deal because the expected value is positive.

No, you should not take the deal because the expected value is negative.

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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