1. Waiting time. Let the time waiting in line, in minutes, be described by the random variable X which has the following pdf, x, 2< x < 4, f(x) 0, otherwise. density, pdf f(x) probability, cdf F(x) 1 probability less than 3 = area under curve, P(X < 3) = 5/12 probability = value of function, F(3) = P(X < 3) = 5/12 2/3 0.75 1/2 probability at 3, P(X = 3) = 0 1/3 0.25+ 4 2 4 X Figure 3.3: f(x) and F(x) Section 2. Definitions (LECTURE NOTES 5) (a) Verify function f(x) satisfies the second property of pdfs,

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...
icon
Related questions
Question
1. Waiting time.
Let the time waiting in line, in minutes, be described by the random variable
X which has the following pdf,
x, 2 < x < 4,
f (x) =
0,
otherwise.
density, pdf f(x)
14
probability, cdf F(x)
probability less than 3
= area under curve,
probability =
value of function,
F(3) = P(X < 3) = 5/12
2/3
0.75
P(X < 3) = 5/12
1/2
probability at 3,
P(X = 3) = 0
1/3
0.25+
X
2
3
4
Figure 3.3: f(x) and F(x)
Section 2. Definitions (LECTURE NOTES 5)
(a) Verify function f(x) satisfies the second property of pdfs,
Transcribed Image Text:1. Waiting time. Let the time waiting in line, in minutes, be described by the random variable X which has the following pdf, x, 2 < x < 4, f (x) = 0, otherwise. density, pdf f(x) 14 probability, cdf F(x) probability less than 3 = area under curve, probability = value of function, F(3) = P(X < 3) = 5/12 2/3 0.75 P(X < 3) = 5/12 1/2 probability at 3, P(X = 3) = 0 1/3 0.25+ X 2 3 4 Figure 3.3: f(x) and F(x) Section 2. Definitions (LECTURE NOTES 5) (a) Verify function f(x) satisfies the second property of pdfs,
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Similar questions
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON