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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. y = Verify the area under the curve is equal to 1. Choose the correct explanation below. A. b-a O B. The area under the curve is the area of the rectangle. (b-a) (b-a) 2 OC. The area under the curve is sum of the maximum and minimum. a+b=0+1=1 The area under the curve is two times the mean. 2- b²a): = 1 = 1 1 b-a Show that the value of the function can never be negative. Choose the correct explanation below. OA. The numerator of the probability density function is 1, so the function must always be positive. OB. The denominator of the probability density function is always positive because a 0, therefore the function must always be positive. OC. The value of b-a is less than one, therefore the value of the function must always be greater than 1.

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. y = Verify the area under the curve is equal to 1. Choose the correct explanation below. A. b-a O B. The area under the curve is the area of the rectangle. (b-a) (b-a) 2 OC. The area under the curve is sum of the maximum and minimum. a+b=0+1=1 The area under the curve is two times the mean. 2- b²a): = 1 = 1 1 b-a Show that the value of the function can never be negative. Choose the correct explanation below. OA. The numerator of the probability density function is 1, so the function must always be positive. OB. The denominator of the probability density function is always positive because a 0, therefore the function must always be positive. OC. The value of b-a is less than one, therefore the value of the function must always be greater than 1.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 1E
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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 ≤x≤b 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. y = Verify the area under the curve is equal to 1. Choose the correct explanation below. A. 1 b-a O B. The area under the curve is the area of the rectangle. (b-a) (b-a) 2 OC. The area under the curve is sum of the maximum and minimum. a+b=0+1=1 The area the curve times the mean. 2- (b-a)= = 1 = 1 1. b-a Show that the value of the function can never be negative. Choose the correct explanation below. O A. The numerator of the probability density function is 1, so the function must always be positive. OB. The denominator of the probability density function is always positive because a <b, so b-a>0, therefore the function must always be positive. OC. The value of b - a is less than one, therefore the value of the function must always be greater than 1.
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 ≤x≤b 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. y = Verify the area under the curve is equal to 1. Choose the correct explanation below. A. 1 b-a O B. The area under the curve is the area of the rectangle. (b-a) (b-a) 2 OC. The area under the curve is sum of the maximum and minimum. a+b=0+1=1 The area the curve times the mean. 2- (b-a)= = 1 = 1 1. b-a Show that the value of the function can never be negative. Choose the correct explanation below. O A. The numerator of the probability density function is 1, so the function must always be positive. OB. The denominator of the probability density function is always positive because a <b, so b-a>0, therefore the function must always be positive. OC. The value of b - a is less than one, therefore the value of the function must always be greater than 1.
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