Q. 4.31 A jar contains m+n聽chips, numbe... [FREE SOLUTION]

91影视

A First Course in Probability

Sheldon M. Ross

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 432 pages

ISBN: 9780321794772

Chapter 4: Q. 4.31 (page 172)

A jar contains $m + n$ chips, numbered $1, 2, 鈥�, n + m$ . A set of size $n$ is drawn. If we let $X$ denote the number of chips drawn having numbers that exceed each of the numbers of those remaining, compute the probability mass function of $X$ .

Short Answer

Expert verified

$P (X = k) = \frac{(\begin{matrix} n + m - k - 1 \\ n - k \end{matrix})}{(\begin{matrix} n + m \\ n \end{matrix})}$

Step by step solution

Given information

A jar contains $m + n$ chips, numbered $1, 2, 鈥�, n + m$ . A set of size $n$ is drawn.

Explanation

Observe that $X 鈭� {0, 鈥�, n}$ . Take any $k 鈭� {0, 鈥�, n}$ . Let's calculate $P (X = k)$ . Observe that there are $(\begin{matrix} n + m \\ n \end{matrix})$ of all possible combinations of taken chips. If $X = k$ , that means that we have taken $k$ largest number, have not taken $(k + 1) s t$ largest number and all other remaining $n - k$ numbers out of remaining $n + m - k - 1$ numbers have been taken freely.

Final answer

The probability mass function is

$P (X = k) = \frac{(\begin{matrix} n + m - k - 1 \\ n - k \end{matrix})}{(\begin{matrix} n + m \\ n \end{matrix})}$

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91影视

A jar contains $m + n$ chips, numbered $1, 2, 鈥�, n + m$ . A set of size $n$ is drawn. If we let $X$ denote the number of chips drawn having numbers that exceed each of the numbers of those remaining, compute the probability mass function of $X$ .

Short Answer

Step by step solution

Given information

Explanation

Final answer

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91影视

A jar contains m+nchips, numbered 1,2,鈥�,n+m. A set of size nis drawn. If we let X denote the number of chips drawn having numbers that exceed each of the numbers of those remaining, compute the probability mass function of X.

Short Answer

Step by step solution

Given information

Explanation

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Mechanics Maths

Pure Maths

Geometry

Calculus

Study anywhere. Anytime. Across all devices.

A jar contains $m + n$ chips, numbered $1, 2, 鈥�, n + m$ . A set of size $n$ is drawn. If we let $X$ denote the number of chips drawn having numbers that exceed each of the numbers of those remaining, compute the probability mass function of $X$ .