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Description: A certain hurricane database extends back to 1851, recording among other data the number of major hurricanes (measuring at least a Category 3) striking a certain region per year. The following table provides a probability distribution for the numb

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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A certain hurricane database extends back to 1851, recording among other data the number of major hurricanes (measuring at least a Category 3) striking a certain region per year. The following table provides a probability distribution for the number of major hurricanes, Y, for a randomly selected year between 1851 and 2012.

y	P(Y=y)	y	P(Y=y)
0	0.186	5	0.041
1	0.252	6	0.027
2	0.246	7	0.011
3	0.094	8	0.104
4	0.039

f. Use the special addition rule and the probability distribution to determine the probability that the year had between

3 and 5 major hurricanes, inclusive.

The probability is_______

The table below shows the probability distribution of the random variable X.

x	1	2	3
P(X=x)	0.3	0.1	0.6

Obtain the standard deviation σ of the random variable.

σ=________

The random variable X is the crew size of a randomly selected shuttle mission. Its probability distribution is shown below. Complete parts a through c.

x	2	4	5	6	7	8
P(X=x)	0.035	0.032	0.324	0.168	0.435	0.006

a. Find and interpret the mean of the random variable.

μ=______

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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