4) Let X₁, X₂,..., Xn be mutually independent and identically distributed continu random variables with the following density function, for 0

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
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4)
Let X₁, X₂,..., Xn be mutually independent and identically distributed continuous
random variables with the following density function,
f(x) = {630x*(1-x)¹ for 0 < x < 1
0,
otherwise
a)
Use the Chebychev inequality to find the value of k, for P(0.2 ≤ x ≤ 0.8).
b) What is the upper and lower bound of P(0.2 < X < 0.8)?
c) Use the central limit theorem to find P(9.5 ≤X ≤ 10.5).
Transcribed Image Text:4) Let X₁, X₂,..., Xn be mutually independent and identically distributed continuous random variables with the following density function, f(x) = {630x*(1-x)¹ for 0 < x < 1 0, otherwise a) Use the Chebychev inequality to find the value of k, for P(0.2 ≤ x ≤ 0.8). b) What is the upper and lower bound of P(0.2 < X < 0.8)? c) Use the central limit theorem to find P(9.5 ≤X ≤ 10.5).
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