Section II 14. An urn has 3 red marbles, 2 white marbles, and 2 blue mar- bles. Marbles are sampled, without replacement, until obtaining a red marble. before finding the first red marble. Let X denote the number of marbles that must be sampled (a) table below. Show that the values of the pmf of X are as given in the xf(x) 3/7 2/7 2 6/35 3 3/35 4 1/35 0. 1
Section II 14. An urn has 3 red marbles, 2 white marbles, and 2 blue mar- bles. Marbles are sampled, without replacement, until obtaining a red marble. before finding the first red marble. Let X denote the number of marbles that must be sampled (a) table below. Show that the values of the pmf of X are as given in the xf(x) 3/7 2/7 2 6/35 3 3/35 4 1/35 0. 1
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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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:(b) Compute the expected number of marbles that must be sampled before finding the first red marble.
![### Section II
14. An urn has 3 red marbles, 2 white marbles, and 2 blue marbles. Marbles are sampled, without replacement, until obtaining a red marble. Let \( X \) denote the number of marbles that must be sampled **before** finding the first red marble.
(a) **[Instructor's Note]** Show that the values of the probability mass function (pmf) of \( X \) are as given in the table below.
| \( x \) | \( f(x) \) |
|---------|------------|
| 0 | \( \frac{3}{7} \) |
| 1 | \( \frac{2}{7} \) |
| 2 | \( \frac{6}{35} \) |
| 3 | \( \frac{3}{35} \) |
| 4 | \( \frac{1}{35} \) |](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F653b506a-bf1f-413c-8a44-59b8a78c6c88%2F111f96f5-5154-4cc3-a895-01ed4c4e0a85%2Fo8awpze_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Section II
14. An urn has 3 red marbles, 2 white marbles, and 2 blue marbles. Marbles are sampled, without replacement, until obtaining a red marble. Let \( X \) denote the number of marbles that must be sampled **before** finding the first red marble.
(a) **[Instructor's Note]** Show that the values of the probability mass function (pmf) of \( X \) are as given in the table below.
| \( x \) | \( f(x) \) |
|---------|------------|
| 0 | \( \frac{3}{7} \) |
| 1 | \( \frac{2}{7} \) |
| 2 | \( \frac{6}{35} \) |
| 3 | \( \frac{3}{35} \) |
| 4 | \( \frac{1}{35} \) |
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