### Probability Distribution for the Sum of Two DiceThe 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:\[ \text{Standard Deviation} = \sqrt{\text{Var}(X)} \]

Answered: 2. The random variable X is sum of 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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I. TRUE OR FALSE. Choose A if the statement is always true, otherwise choose B. 1. The sum of the probabilities of all values of the random variable must be equal to 1. 2. The capacity of water dams in a region is an example of continuous random variable. 3. The formula u = is used to compute for the mean of a probability distribution. IxF(x) 4. A standard normal curve is a normal probability distribution that has a mean of one and standard deviation of one 5. The width of the curve in normal distribution is determined by the mean of the distribution. 6. The mean of the sampling distribution of the sample means is less than the population mean. 7. The standard error of the mean is the standard deviation of the sampling distribution of the sample means. 8. The sampling variability of the sample means becomes smaller as the sample size n gets larger. 9. In estimating the mean, the degrees of freedom is equal to (n - 1) when using the t- distribution. 10. The t-distribution is asymmetric…
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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.