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A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a 0, therefore the function must always be positive OC. The numerator of the probability density function is 1, so the function must always be positive.

A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a 0, therefore the function must always be positive OC. The numerator of the probability density function is 1, so the function must always be positive.

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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A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a < b), where a sxsb and all of the values of x are equally likely to occur. The graph of a uniform distribution is shown to the right. The probability density function of a uniform distribution is shown below. Show that the probability density function of a uniform distribution satisfies the two conditions for a probability density function. Ay 1 b- a b-a Verify the area under the curve is equal to 1. Choose the correct explanation below. O A. The area under the curve is sum of the maximum and minimum, a + b = 0 + 1= 1 O B. The area under the curve is two times the mean. 2 (b- a) = 1 Oc. The area under the curve is the area of the rectangle. (b - a) = 1 Show that the value of the function can never be negative. Choose the correct explanation below. O A. The value of b- a is less than one, therefore the value of the function must always be greater than 1. O B. The denominator of the probability density function is always positive because a < b, so b- a>0, therefore the function must always be positive. O C. The numerator of the probability density function is 1, so the function must always be positive. Next P Type here to search DE 47°F Cloudy 6:21 PM 12/20/2021 14 f8 f10 112 prt sc Sysra pause delele backspace PI 00
Transcribed Image Text:A uniform distribution is a continuous probability distribution for a random variable x between two values a and b (a < b), where a sxsb and all of the values of x are equally likely to occur. The graph of a uniform distribution is shown to the right. The probability density function of a uniform distribution is shown below. Show that the probability density function of a uniform distribution satisfies the two conditions for a probability density function. Ay 1 b- a b-a Verify the area under the curve is equal to 1. Choose the correct explanation below. O A. The area under the curve is sum of the maximum and minimum, a + b = 0 + 1= 1 O B. The area under the curve is two times the mean. 2 (b- a) = 1 Oc. The area under the curve is the area of the rectangle. (b - a) = 1 Show that the value of the function can never be negative. Choose the correct explanation below. O A. The value of b- a is less than one, therefore the value of the function must always be greater than 1. O B. The denominator of the probability density function is always positive because a < b, so b- a>0, therefore the function must always be positive. O C. The numerator of the probability density function is 1, so the function must always be positive. Next P Type here to search DE 47°F Cloudy 6:21 PM 12/20/2021 14 f8 f10 112 prt sc Sysra pause delele backspace PI 00
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