Let X be a random variable with CDF Fx (x)=x³ for 0 ≤ x ≤ 1. Find: a) P (X > ¹); b) the density function fx (x); c) E(X). d) Let Y₁, Y2, Y3 be three points chosen independently and uniformly on the unit interval [0, 1], and let X be the rightmost point of them. Show that X has the distribution described above.
Let X be a random variable with CDF Fx (x)=x³ for 0 ≤ x ≤ 1. Find: a) P (X > ¹); b) the density function fx (x); c) E(X). d) Let Y₁, Y2, Y3 be three points chosen independently and uniformly on the unit interval [0, 1], and let X be the rightmost point of them. Show that X has the distribution described above.
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.CR: Chapter 13 Review
Problem 30CR
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![Let X be a random variable with CDF Fx(x) = x³ for 0 ≤ x ≤ 1. Find:
a) P (X ≥ ¹);
b) the density function fx(x);
c) E(X).
d) Let Y₁, Y2, Y3 be three points chosen independently and uniformly on the unit interval [0, 1], and
let X be the rightmost point of them. Show that X has the distribution described above.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F76eec8ec-d87c-4fdd-96a3-96e8325f09a2%2F7ac0a681-4d19-4608-a9f1-ffd60009b808%2F8hr89en_processed.png&w=3840&q=75)
Transcribed Image Text:Let X be a random variable with CDF Fx(x) = x³ for 0 ≤ x ≤ 1. Find:
a) P (X ≥ ¹);
b) the density function fx(x);
c) E(X).
d) Let Y₁, Y2, Y3 be three points chosen independently and uniformly on the unit interval [0, 1], and
let X be the rightmost point of them. Show that X has the distribution described above.
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