2. The random variable X is sum of the dice when 2 balanced dice are rolled. 2 3 4 7 8 9. 10 11 12 P(X=x) 1/36 1/18 1/12 1/9 5/36 1/6 5/36 1/9 1/12 1/18 1/36 g. Find the mean of the sum of the dice. h. Find the standard deviation for the sum of the dice.
2. The random variable X is sum of the dice when 2 balanced dice are rolled. 2 3 4 7 8 9. 10 11 12 P(X=x) 1/36 1/18 1/12 1/9 5/36 1/6 5/36 1/9 1/12 1/18 1/36 g. Find the mean of the sum of the dice. h. Find the standard deviation for the sum of the dice.
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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![### Probability Distribution for the Sum of Two Dice
The random variable \( X \) represents the sum of the numbers on two balanced dice when rolled. The probability distribution table for \( X \) is as follows:
| \( X \) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|--------------|------|------|------|------|------|------|------|------|------|------|------|
| \( P(X=x) \) | 1/36 | 1/18 | 1/12 | 1/9 | 5/36 | 1/6 | 5/36 | 1/9 | 1/12 | 1/18 | 1/36 |
#### Tasks:
**g. Find the mean of the sum of the dice.**
To find the mean (or expected value) \( E(X) \) of the sum of the dice, use the formula:
\[ E(X) = \sum (x \cdot P(X=x)) \]
**h. Find the standard deviation for the sum of the dice.**
First, find the variance \( \text{Var}(X) \) using:
\[ \text{Var}(X) = \sum (x^2 \cdot P(X=x)) - [E(X)]^2 \]
Then, calculate the standard deviation by taking the square root of the variance:
\[ \text{Standard Deviation} = \sqrt{\text{Var}(X)} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0ba38191-1dc1-457f-9377-4b46cb7e2378%2F8ac4f844-7708-4299-a67e-a0ddbc6a96d3%2Fwj32h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Probability Distribution for the Sum of Two Dice
The random variable \( X \) represents the sum of the numbers on two balanced dice when rolled. The probability distribution table for \( X \) is as follows:
| \( X \) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|--------------|------|------|------|------|------|------|------|------|------|------|------|
| \( P(X=x) \) | 1/36 | 1/18 | 1/12 | 1/9 | 5/36 | 1/6 | 5/36 | 1/9 | 1/12 | 1/18 | 1/36 |
#### Tasks:
**g. Find the mean of the sum of the dice.**
To find the mean (or expected value) \( E(X) \) of the sum of the dice, use the formula:
\[ E(X) = \sum (x \cdot P(X=x)) \]
**h. Find the standard deviation for the sum of the dice.**
First, find the variance \( \text{Var}(X) \) using:
\[ \text{Var}(X) = \sum (x^2 \cdot P(X=x)) - [E(X)]^2 \]
Then, calculate the standard deviation by taking the square root of the variance:
\[ \text{Standard Deviation} = \sqrt{\text{Var}(X)} \]
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