Suppose you have an experiment where you toss a fair coin three times. You then count the number of heads observed over those three tosses. Use this experiment to address each of the following questions. Round solutions to three decimal places, if necessary.
Suppose you have an experiment where you toss a fair coin three times. You then count the number of heads observed over those three tosses. Use this experiment to address each of the following questions. Round solutions to three decimal places, if necessary.
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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I need assistance with parts D, E,, F please, thank you
![**Title: Understanding Probability Distributions Using Coin Toss Experiments**
**Experiment Overview:**
Suppose you have an experiment where you toss a fair coin three times. You then count the number of heads observed over these three tosses. This experiment will be used to address the following questions. Solutions should be rounded to three decimal places if necessary.
**a) State the Random Variable:**
- Random Variable: \( X = \) the number of heads observed when you flip a coin three times.
**b) Construct a Probability Distribution Table:**
The probability distribution table for the number of heads obtained over three tosses is shown below:
| x | \( P(x) \) |
|---|--------|
| 0 | 0.125 |
| 1 | 0.375 |
| 2 | 0.375 |
| 3 | 0.125 |
**c) Determine the Shape of the Probability Distribution:**
- The probability distribution of \( x \) is **Symmetric**.
**d) Find the Mean Number of Heads for this Distribution:**
- Calculate the mean (\( \mu \)): \[ \mu = \sum [x \cdot P(x)] \]
\[ \mu = (0 \times 0.125) + (1 \times 0.375) + (2 \times 0.375) + (3 \times 0.125) \]
\[ \mu = 0 + 0.375 + 0.75 + 0.375 \]
\[ \mu = 1.5 \]
The mean of a discrete probability distribution is also denoted by \( \mu \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec7d0b78-7026-4f2e-9cd3-9f6affde891c%2F84fc02c0-7ed7-454a-937b-58eae87ce6dc%2Fyeg0mo6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Probability Distributions Using Coin Toss Experiments**
**Experiment Overview:**
Suppose you have an experiment where you toss a fair coin three times. You then count the number of heads observed over these three tosses. This experiment will be used to address the following questions. Solutions should be rounded to three decimal places if necessary.
**a) State the Random Variable:**
- Random Variable: \( X = \) the number of heads observed when you flip a coin three times.
**b) Construct a Probability Distribution Table:**
The probability distribution table for the number of heads obtained over three tosses is shown below:
| x | \( P(x) \) |
|---|--------|
| 0 | 0.125 |
| 1 | 0.375 |
| 2 | 0.375 |
| 3 | 0.125 |
**c) Determine the Shape of the Probability Distribution:**
- The probability distribution of \( x \) is **Symmetric**.
**d) Find the Mean Number of Heads for this Distribution:**
- Calculate the mean (\( \mu \)): \[ \mu = \sum [x \cdot P(x)] \]
\[ \mu = (0 \times 0.125) + (1 \times 0.375) + (2 \times 0.375) + (3 \times 0.125) \]
\[ \mu = 0 + 0.375 + 0.75 + 0.375 \]
\[ \mu = 1.5 \]
The mean of a discrete probability distribution is also denoted by \( \mu \).
![**Understanding Discrete Probability Distributions**
1. **Mean Notation**
- The mean of a discrete probability distribution is also notated by:
- (Dropdown: Select an answer)
2. **Interpretation of the Mean**
- Which of the following is the correct interpretation of the mean?
- (Dropdown: Select an answer)
3. **Calculating Standard Deviation**
e) **Find the Standard Deviation**
- Calculate the standard deviation (\(\sigma\)) for the number of heads within this distribution.
- \(\sigma =\) [Input Box]
4. **Probability Calculation**
f) **Probability of One or Less Heads**
- Calculate the probability of obtaining one or less heads over three tosses of a coin:
- \(P\)(one or less heads) = [Input Box]
**Additional Resources**
- **Question Help:**
- [Video] (Link to instructional video)
**Submission**
- [Submit All Parts] (Button)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec7d0b78-7026-4f2e-9cd3-9f6affde891c%2F84fc02c0-7ed7-454a-937b-58eae87ce6dc%2F40zktf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Discrete Probability Distributions**
1. **Mean Notation**
- The mean of a discrete probability distribution is also notated by:
- (Dropdown: Select an answer)
2. **Interpretation of the Mean**
- Which of the following is the correct interpretation of the mean?
- (Dropdown: Select an answer)
3. **Calculating Standard Deviation**
e) **Find the Standard Deviation**
- Calculate the standard deviation (\(\sigma\)) for the number of heads within this distribution.
- \(\sigma =\) [Input Box]
4. **Probability Calculation**
f) **Probability of One or Less Heads**
- Calculate the probability of obtaining one or less heads over three tosses of a coin:
- \(P\)(one or less heads) = [Input Box]
**Additional Resources**
- **Question Help:**
- [Video] (Link to instructional video)
**Submission**
- [Submit All Parts] (Button)
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