Answered: you take 5 draws from U(9,15). Consider…

you take 5 draws from U(9,15). Consider the random variable that equals the 2nd smallest of the 5 draws. What is the probability that this random variable is greater than 10?

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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Question

you take 5 draws from U(9,15). Consider the random variable that equals the 2nd smallest of the 5 draws. What is the probability that this random variable is greater than 10?

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Expert Solution

Step 1

Let $X_{1,} X_{2}, X_{3}, X_{4}, X_{5}$ be the sample drawn from the distribution $U (9, 15)$ . Denote the order statistics for it as follows:

$X_{(1)} = min (X_{1,} X_{2}, X_{3}, X_{4}, X_{5}) X_{(2)} = {the 2}^{n d} s m a l l e s t X_{(3)} = {the 3}^{r d} i n o r d e r X_{(4)} = {the 4}^{t h} i n o r d e r X_{(5)} = max (X_{1,} X_{2}, X_{3}, X_{4}, X_{5})$

To find the probability of $X_{(2)} \geq 10$ , first, it is required to define the pdf of $X_{(2)}$ . Recall that the pdf is the probability of a random variable taking a particular value.

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