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 six sided die. If you roll a 6, you win $16. If you roll a 4 or 5, you win $1. Otherwise, you pay $2. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table X P(X) b. Find the expected profit. $ (Round to the nearest cent) c. Interpret the expected value. You will win this much if you play a game. If you play many games you will likely win on average very close to $2.00 per game. This is the most likely amount of money you will win. d. Based on the expected value, should you play this game? Yes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost. No, since the expected value is negative, you would be very likely to come home with less money if you played many games. Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. No, this is a gambling game and it is always a bad idea to gamble. Yes, because you can win $16.00 which is greater than the $2.00 that you can lose.

# Probability Distribution Table

## Explanation

This table is used to represent the probability distribution of a discrete random variable $X$. Each possible value of $X$ is listed along with its corresponding probability $P(X)$.

## Table Structure

### Headers:
- **X**: This column represents the possible values of the discrete random variable $X$.
- **P(X)**: This column represents the probability corresponding to each value of $X$. The sum of all these probabilities should equal 1.

### Rows:
The rows under each header should list the specific values of $X$ and their corresponding probabilities $P(X)$. In this table, there is space for three different values of $X$.

### Example Usage:
Suppose $X$ denotes the outcome of rolling a fair six-sided die. The table might look like the following:

| X | P(X) |
|---|------|
| 1 | 1/6 |
| 2 | 1/6 |
| 3 | 1/6 |
| 4 | 1/6 |
| 5 | 1/6 |
| 6 | 1/6 |

In this example, each value from 1 to 6 (possible outcomes of the die) is equally likely with a probability of $\frac{1}{6}$.

In the provided table, you can fill in the specific values for your case, ensuring that the sum of all probabilities $P(X)$ equals 1.

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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