Q5 Let = {} 1 91 (3₁) = f(x) = x = 1, 2, 3, 4, 5, 6, otherwise. be the probability mass function of a discrete random variable X. Show that the probability mass function of the smallest observation Y₁ of a random sample of size 5 from this distribution is 5 - (²= ")" - (0 ="), y = 1, 2, 3, 4, 5, 6. 6 and zero otherwise. Note: you already know how to write down the cumulative distribution function of Y₁, the smallest of X₁, X₂, X3, X4, and X5; remembering that we are sampling from a discrete distribution, derive the probability mass function of Y₁.
Q5 Let = {} 1 91 (3₁) = f(x) = x = 1, 2, 3, 4, 5, 6, otherwise. be the probability mass function of a discrete random variable X. Show that the probability mass function of the smallest observation Y₁ of a random sample of size 5 from this distribution is 5 - (²= ")" - (0 ="), y = 1, 2, 3, 4, 5, 6. 6 and zero otherwise. Note: you already know how to write down the cumulative distribution function of Y₁, the smallest of X₁, X₂, X3, X4, and X5; remembering that we are sampling from a discrete distribution, derive the probability mass function of Y₁.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Q5 Let
= {}
1
f(x) =
x = 1, 2, 3, 4, 5, 6,
otherwise.
be the probability mass function of a discrete random variable X. Show that the probability mass function of the smallest observation Y₁ of a
random sample of size 5 from this distribution is
5
91 (y₁) = = (²-")" - (0 =³) "₁
6
6
y = 1, 2, 3, 4, 5, 6.
and zero otherwise. Note: you already know how to write down the cumulative distribution function of Y₁, the smallest of X₁, X₂, X3, X₁, and
X5; remembering that we are sampling from a discrete distribution, derive the probability mass function of Y₁.
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