The answer choices for expected value of x is E(X):0.5610.5310.5500.697The answer choices for the standard deviation of the random variable X, denoted σ,:0.80.60.70.9 and which player is more likely to help the team score runs The image contains a histogram chart and accompanying text related to baseball statistics.### Histogram Chart Explanation- **Title:** Probability Distribution- **Axes:** - **x-axis (x):** Represents the number of bases advanced (0 through 4). - **y-axis (P(x)):** Represents the probability of advancing the respective number of bases. - **Bars:** - **x = 0:** Probability approximately 0.62 - **x = 1:** Probability approximately 0.28 - **x = 2:** Probability barely 0.06 - **x = 3 and 4:** Probability less than 0.04### Accompanying Text**Analysis and Calculation:**Based solely on this graph:- The expected value $ E(X) $, representing the expected number of bases advanced, is stated to be **between 0 and 1**.**Calculation Instructions:**1. **Expected Value (E(X)):** - Calculate using values of $ P(x) $ rounded to three decimal places.2. **Standard Deviation ($ \sigma $):** - Calculate for the random variable $ X $ using values of $ P(x) $ rounded to three decimal places. **Scenario and Decision-Making:**- You are tasked with selecting players for an all-star baseball team. Choosing between Derek Jeter and Sammy Sosa: - Probability distribution for Sammy Sosa gives $ E(X) = 0.514 $ and $ \sigma = 0.959 $. **Choices:**- Pick Derek Jeter.- Pick Sammy Sosa.- Conclude that both players are equally likely to help the all-star team score. This content is designed to help make statistical decisions based on probability distributions in sports analytics. ### 2. Expected Value and Variance of a Discrete Random VariableDerek Jeter, a Major League Baseball player, was a shortstop for the New York Yankees in 2007. Consider the experiment of Jeter making a batting appearance. There are five experimental outcomes: he is out, he advances to first base, hits a double, hits a triple, or hits a home run. Define the random variable $X$ as the number of bases that Jeter advances on the baseball diamond from his batting appearance. Thus, the values of $X$ are:- $x = 0$ if he is out- $x = 1$ if he advances to first base- $x = 2$ if he hits a double- $x = 3$ if he hits a triple- $x = 4$ if he hits a home runJeter’s hitting statistics for the regular 2007 baseball season were used to construct the following table:| Experimental Outcome | $x$ | Number of Occurrences during the 2007 Season² | $P(x)$ ||----------------------|-------|-----------------------------------------------|----------|| Out | 0 | 420 | 0.588 || Advances to first base¹ | 1 | 239 | 0.335 || Double | 2 | 39 | 0.055 || Triple | 3 | 4 | 0.006 || Home run | 4 | 12 | 0.017 |¹Includes a single, walk, hit by pitch, and fielder’s choice, as well as making it safely on base due to an error.²Data source: These data were obtained from the Major League Baseball website, available at www.mlb.com.Use the relative frequency approach to develop the probability distribution of the random variable $X$. Fill in the probability of each value of $X$ using the dropdown menus in the previous table.

OutcomexNumber of occurrencesP(x)Out04200.588Advances to first…

Based solely on this graph, you can conclude that E(X), the expected number of bases advanced, is between 0 and 1 ▼ Now calculate E(X). The expected value of x is E(X) = [Note: For your calculation, use values of P(x) rounded to three decimal places.] The standard deviation of the random variable X, denoted σ, is. [Note: For your calculation, use values of P(x) rounded to three decimal places.] Suppose that you are responsible for selecting players for an all-star baseball team, and you have to choose between Derek Jeter and Sammy Sosa, the former designated hitter for the Texas Rangers. You develop a probability distribution for Sammy Sosa and find that E(X) = 0.514 and σ = 0.959. You are looking for the player who is more likely to help the team score runs. What do you do? O Pick Derek Jeter. O Pick Sammy Sosa. O Throw up your hands, because Jeter and Sosa are equally likely to help the all-star team score.

Based solely on this graph, you can conclude that E(X), the expected number of bases advanced, is between 0 and 1 ▼ Now calculate E(X). The expected value of x is E(X) = [Note: For your calculation, use values of P(x) rounded to three decimal places.] The standard deviation of the random variable X, denoted σ, is. [Note: For your calculation, use values of P(x) rounded to three decimal places.] Suppose that you are responsible for selecting players for an all-star baseball team, and you have to choose between Derek Jeter and Sammy Sosa, the former designated hitter for the Texas Rangers. You develop a probability distribution for Sammy Sosa and find that E(X) = 0.514 and σ = 0.959. You are looking for the player who is more likely to help the team score runs. What do you do? O Pick Derek Jeter. O Pick Sammy Sosa. O Throw up your hands, because Jeter and Sosa are equally likely to help the all-star team score.

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

The answer choices for expected value of x is E(X):

0.561
0.531
0.550
0.697

The answer choices for the standard deviation of the random variable X, denoted σ,:

0.8
0.6
0.7
0.9

and which player is more likely to help the team score runs

The image contains a histogram chart and accompanying text related to baseball statistics.

### Histogram Chart Explanation

- **Title:** Probability Distribution
- **Axes:**
- **x-axis (x):** Represents the number of bases advanced (0 through 4).
- **y-axis (P(x)):** Represents the probability of advancing the respective number of bases.

- **Bars:**
- **x = 0:** Probability approximately 0.62
- **x = 1:** Probability approximately 0.28
- **x = 2:** Probability barely 0.06
- **x = 3 and 4:** Probability less than 0.04

### Accompanying Text

**Analysis and Calculation:**

Based solely on this graph:
- The expected value $ E(X) $, representing the expected number of bases advanced, is stated to be **between 0 and 1**.

**Calculation Instructions:**

1. **Expected Value (E(X)):**
- Calculate using values of $ P(x) $ rounded to three decimal places.

2. **Standard Deviation ($ \sigma $):**
- Calculate for the random variable $ X $ using values of $ P(x) $ rounded to three decimal places.

**Scenario and Decision-Making:**

- You are tasked with selecting players for an all-star baseball team. Choosing between Derek Jeter and Sammy Sosa:
- Probability distribution for Sammy Sosa gives $ E(X) = 0.514 $ and $ \sigma = 0.959 $.

**Choices:**

- Pick Derek Jeter.
- Pick Sammy Sosa.
- Conclude that both players are equally likely to help the all-star team score.

This content is designed to help make statistical decisions based on probability distributions in sports analytics.

### 2. Expected Value and Variance of a Discrete Random Variable

Derek Jeter, a Major League Baseball player, was a shortstop for the New York Yankees in 2007. Consider the experiment of Jeter making a batting appearance. There are five experimental outcomes: he is out, he advances to first base, hits a double, hits a triple, or hits a home run. Define the random variable $X$ as the number of bases that Jeter advances on the baseball diamond from his batting appearance. Thus, the values of $X$ are:

- $x = 0$ if he is out
- $x = 1$ if he advances to first base
- $x = 2$ if he hits a double
- $x = 3$ if he hits a triple
- $x = 4$ if he hits a home run

Jeter’s hitting statistics for the regular 2007 baseball season were used to construct the following table:

| Experimental Outcome | $x$ | Number of Occurrences during the 2007 Season² | $P(x)$ |
|----------------------|-------|-----------------------------------------------|----------|
| Out | 0 | 420 | 0.588 |
| Advances to first base¹ | 1 | 239 | 0.335 |
| Double | 2 | 39 | 0.055 |
| Triple | 3 | 4 | 0.006 |
| Home run | 4 | 12 | 0.017 |

¹Includes a single, walk, hit by pitch, and fielder’s choice, as well as making it safely on base due to an error.

²Data source: These data were obtained from the Major League Baseball website, available at www.mlb.com.

Use the relative frequency approach to develop the probability distribution of the random variable $X$. Fill in the probability of each value of $X$ using the dropdown menus in the previous table.

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