Need help ONLY with parts (c), (d), and (e) on this Intro to probability and statistics homework problem. Below the homework problem is the answers from the textbook. Make sure your handwriting is neat and readable. 4.1-11. A manufactured item is classified as good, a "sec-ond." or defective with probabilities 6/10, 3/10, and 1/10.respectively. Fifteen such items are selected at randomfrom the production line. Let X denote the number ofgood items, Y the number of seconds, and 15 - X - Ythe number of defective items.(a) Give the joint pmf of X and Y, f(x, y).(b) Sketch the set of points for which f(x, y) > 0. Fromthe shape of this region, can X and Y be independent?Why or why not?(c) Find P(X= 10, Y = 4).(d) Give the marginal pmf of X.(e) Find P(X ≤ 11). 4.1-11 (a) f(x, y) =15!xly! (15-x-y)! 10()))100≤x+y≤ 15:(b) No, because the space is not rectangular;(c) 0.0735;(d) X is b(15,0.6);(e) 0.9095.15-8-y

Given Information: Probability that an item is good is 610. Probability that an item is a second is…

Math

Probability

(c) Find P(X= 10, Y = 4). (d) Give the marginal pmf of X. (e) Find P(X 11).

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

Need help ONLY with parts (c), (d), and (e) on this Intro to probability and statistics homework problem. Below the homework problem is the answers from the textbook. Make sure your handwriting is neat and readable.

4.1-11. A manufactured item is classified as good, a "sec-
ond." or defective with probabilities 6/10, 3/10, and 1/10.
respectively. Fifteen such items are selected at random
from the production line. Let X denote the number of
good items, Y the number of seconds, and 15 - X - Y
the number of defective items.
(a) Give the joint pmf of X and Y, f(x, y).
(b) Sketch the set of points for which f(x, y) > 0. From
the shape of this region, can X and Y be independent?
Why or why not?
(c) Find P(X= 10, Y = 4).
(d) Give the marginal pmf of X.
(e) Find P(X ≤ 11).

4.1-11 (a) f(x, y) =
15!
xly! (15-x-y)! 10
()))
10
0≤x+y≤ 15:
(b) No, because the space is not rectangular;
(c) 0.0735;
(d) X is b(15,0.6);
(e) 0.9095.
15-8-y

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