why not? s section, we argued that if Y is continuous and a
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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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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Please how do i solve 4.10?
Transcribed Image Text:herbari
opties
4.10
4.11
4.12
b Use Table 1, Appendix 3, to obtain P(2< Y ≤ 5) and P(2 ≤ Y≤ 5). Are these two
probabilities equal? Why or why not?
C
4.8 Suppose that Y has density function
b
c
Earlier in this section, we argued that if Y is continuous and a <b, then P(a <Y < b) =
P(a ≤Y < b). Does the result in part (a) contradict this claim? Why?
Find P(.4 ≤ y ≤ 1).
Find P(.4 ≤Y < 1).
Find P(Y ≤.4|Y ≤.8).
e Find P(Y <.4|Y <.8).
4.9 A random variable Y has the following distribution function:
0,
for y < 2,
1/8,
for 2 ≤ y ≤ 2.5,
3/16,
for 2.5 ≤ y < 4,
F(y) = P(Y ≤ y) = 1/2
5/8,
11/16,
1,
a
Is Y a continuous or discrete random variable? Why?
b What values of Y are assigned positive probabilities?
с Find the probability function for Y.
d What is the median, 5, of Y?
Refer to the density function given in Exercise 4.8.
[ky(1-y), 0≤ y ≤ 1,
elsewhere.
f(y) =
= {kx (²-
a Find the value of k that makes f(y) a probability density function.
b
c
d
f(y) =
a Find the .95-quantile, 95, such that P(Y ≤ 95) = .95.
Find a value yo so that P(Y<yo) = .95.
Compare the values for 95 and yo that you obtained in parts (a) and (b). Explain the
relationship between these two values.
is book to
Suppose that Y possesses the density function
cy,
(0,
for 4 ≤ y < 5.5,
for 5.5 ≤ y < 6,
for 6 ≤y <7,
for y ≥ 7.
0≤ y ≤ 2,
elsewhere.
Exercises 167
a
Find the value of c that makes f(y) a probability density function.
b Find F(y).
c
Graph f(y) and F(y).
d
Use F(y) to find P(1 ≤ y ≤ 2).
Use f(y) and geometry to find P(1 ≤ y ≤ 2).
e
The length of time to failure (in hundu. 1
be
Ove
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