Let (N, A, P) = ([0, 1], B([0, 1]), A|[0,1) and define a mapping X : [0, 1] → R by 0

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 20CR: Let T be a linear transformation from R3 into R such that T(1,1,1)=1, T(1,1,0)=2 and T(1,0,0)=3....
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Let (N, A, P) = ([0, 1], B([0, 1]), A|[0,1) and define a mapping X : [0, 1] → R by
0 <w < ;
| sw< };
(w²,
1,
= (m)x
4w?,
sw<1.
a) Justify, why X is a random variable.
b) Determine P(X € [0,1]) and P(X e ,1)).
c) Determine the expected value of Y and the cumulative distribution function of Y, where
Y = VX.
Transcribed Image Text:Let (N, A, P) = ([0, 1], B([0, 1]), A|[0,1) and define a mapping X : [0, 1] → R by 0 <w < ; | sw< }; (w², 1, = (m)x 4w?, sw<1. a) Justify, why X is a random variable. b) Determine P(X € [0,1]) and P(X e ,1)). c) Determine the expected value of Y and the cumulative distribution function of Y, where Y = VX.
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