SOLUTION: If X uniformly distributed over (-1, 1), find
a) P{|X| > 1/2};
b) The density function of the random variable |X|.
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Question 592262: If X uniformly distributed over (-1, 1), find
a) P{|X| > 1/2};
b) The density function of the random variable |X|.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
a)
Draw a rectangle that spans from x = -1 to x = 1. The length is 1 - (-1) = 2 units. The height is then 1/2 because the product of the length and height must be equal to 1.
Now your task is to find the area of the rectangle from x = 1/2 to x = 1
The area is then: (1/2)*(1/2) = 1/4
So P{|X| > 1/2} = 1/4
---------------------------------------------------
b)
From part a), the height of the rectangle is the pdf curve. Since the height is 1/2, the density function is f(x) = 1/2
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