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1) A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

1) A die is rolled 9 times and the number of times that two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos.

MATLAB: An Introduction with Applications
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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**Problem 1: Die Rolling Experiment** A die is rolled 9 times, and the number of times that a two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos. --- **Solution Approach:** To find the mean number of twos in many repetitions of this experiment, consider the following: 1. The probability of rolling a two on a fair die is \( \frac{1}{6} \). 2. Let \( X \) be the random variable representing the number of times a two appears when rolling the die 9 times. 3. \( X \) follows a binomial distribution \( X \sim \text{Binomial}(n=9, p=\frac{1}{6}) \). 4. The mean (expected value) of a binomial distribution is given by \( E(X) = n \cdot p \). 5. Substitute the values: \( E(X) = 9 \cdot \frac{1}{6} = 1.5 \). Therefore, the mean number of times a two is expected to appear is 1.5.
Transcribed Image Text:**Problem 1: Die Rolling Experiment** A die is rolled 9 times, and the number of times that a two shows on the upper face is counted. If this experiment is repeated many times, find the mean for the number of twos. --- **Solution Approach:** To find the mean number of twos in many repetitions of this experiment, consider the following: 1. The probability of rolling a two on a fair die is \( \frac{1}{6} \). 2. Let \( X \) be the random variable representing the number of times a two appears when rolling the die 9 times. 3. \( X \) follows a binomial distribution \( X \sim \text{Binomial}(n=9, p=\frac{1}{6}) \). 4. The mean (expected value) of a binomial distribution is given by \( E(X) = n \cdot p \). 5. Substitute the values: \( E(X) = 9 \cdot \frac{1}{6} = 1.5 \). Therefore, the mean number of times a two is expected to appear is 1.5.
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