Homework SourseA real number is chosen at random from 01 with uniform proba
A real number is chosen at random from [0,1] with uniform probability, and then this number is squared. Let Y represent the result.
What is the density function of Y?
Solution
PDF of Uniform Distribution f(x) = 1 / ( b - a ) for a < x < b
b = Maximum Value
a = Minimum Value
Mean = a + b / 2
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 )
Probability Density function = f(x) = 1/(b-a) = 1 / (1-0) = 1 / 1 = 1
Mean = a + b / 2 = 0.5
Standard Deviation = Sqrt ( ( b - a ) ^ 2 / 12 ) = 0.289
![A real number is chosen at random from [0,1] with uniform probability, and then this number is squared. Let Y represent the result. What is the density function](/WebImages/3/a-real-number-is-chosen-at-random-from-01-with-uniform-proba-976355-1761500860-0.webp "A real number is chosen at random from [0,1] with uniform probability, and then this number is squared. Let Y represent the result. What is the density function")
