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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 probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded. Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property is being illustrated?

The probability distribution of the random variable X represents the number of hits a baseball player obtained in a game for the 2012 baseball season.
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P(x) 0.16790.3424 0.2938 0.1489 0.0380 0.0090
The probability distribution was used along with statistical software to simulate 25 repetitions of the experiment (25 games). The number of hits was recorded.
Approximate the mean and standard deviation of the random variable X based on the simulation. The simulation was repeated by performing 50 repetitions of the
experiment. Approximate the mean and standard deviation of the random variable. Compare your results to the theoretical mean and standard deviation. What property
is being illustrated?
Click the icon to view the data tables.
Data tables
(Round to three decimal places as needed.)
Table of the numbers of hits for 25 games
2 1
1 0
Approximate the mean of the random variable X based on the simulation for 25 games.
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1
4
1
xx 1.440 hits
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1
2
3
1
(Round to three decimal places as needed.)
1
3
4
2 2
1
1
Approximate the standard deviation of the random variable X based on the simulation for 25 games.
Table of the numbers of hits for 50 games
hits
(Round to three decimal places as needed.)
2 1
1
1
1
4
1
3
1 1
2
3
1
0|0
1
3
4
2 2
4 2
1
1
2 |2
2
1
1
1
3
3
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2 0|2
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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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