Explanation Standard deviation for a probability density function on [ a , b ] . The value m such that ∫ a m f ( x ) d x = 1 2 Calculation: Consider, the probability density function f ( x ) = 4 x − 3 x 2 for x in [ 0 , 1 ] . The value m such that, ∫ a m f ( x ) d x = 1 2 Find the value of above probability function, ∫ 0 m ( 4 x − 3 x 2 ) x d x = 0.5 [ 4 x 2 2 − 3 x 3 3 ] 0 m = 0.5 [ 2 x 2 − x 3 ] 0 m = 0.5 Apply the limits of integration, [ 2 m 2 − m 3 ] = 0.5 2 m 2 − m 3 = 0

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Chapter 13.CR, Problem 30CR

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The median of the probability density function for a random variable x is f(x)=4x−3x2 in [0,1] and the probability that the value of the random variable will lie between the median and the mean of the distribution.

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Chapter 13.CR, Problem 29CR

Chapter 13.CR, Problem 31CR

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The median of the probability density function for a random variable x is f ( x ) = 4 x − 3 x 2 in [ 0 , 1 ] and the probability that the value of the random variable will lie between the median and the mean of the distribution.

Solution Summary: The author explains the probability density function of a random variable x, which is defined by the median of the function.

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To find:

The median of the probability density function for a random variable x is f(x)=4x−3x2 in [0,1] and the probability that the value of the random variable will lie between the median and the mean of the distribution.

Want to see the full answer?

Chapter 13 Solutions

The median of the probability density function for a random variable x is f ( x ) = 4 x − 3 x 2 in [ 0 , 1 ] and the probability that the value of the random variable will lie between the median and the mean of the distribution.

Solution Summary: The author explains the probability density function of a random variable x, which is defined by the median of the function.

Concept explainers

Videos

To find: The median of the probability density function for a random variable x is f(x)=4x−3x2 in [0,1] and the probability that the value of the random variable will lie between the median and the mean of the distribution.

Want to see the full answer?

Chapter 13 Solutions

To find:

The median of the probability density function for a random variable x is f(x)=4x−3x2 in [0,1] and the probability that the value of the random variable will lie between the median and the mean of the distribution.