Let X1, X2,..., X25 be independent continuous random variables with the following common cumulative distribution function: x < 0 F,(r) = { 1- (1 – x)3 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Let X1, X2, . .., X25 be independent continuous random variables with the following common cumulative
distribution function:
x < 0
F, (z) = { 1– (1 – x)*
0 < x < 1 .
|
1
x > 1
(a) Find the probability that exactly 3 of these random variables exceed 0.1. Show all the steps. Circle the
final answer.
(b) Use the Central Limit Theorem to approximate P(0.2 < X < 0.35), where X = E X;. Show
25
all the steps. Circle the final answer.
Transcribed Image Text:Let X1, X2, . .., X25 be independent continuous random variables with the following common cumulative distribution function: x < 0 F, (z) = { 1– (1 – x)* 0 < x < 1 . | 1 x > 1 (a) Find the probability that exactly 3 of these random variables exceed 0.1. Show all the steps. Circle the final answer. (b) Use the Central Limit Theorem to approximate P(0.2 < X < 0.35), where X = E X;. Show 25 all the steps. Circle the final answer.
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