Suppose I represents the uncertainty in the number of Delivered Source Instructions (DSI) for a new software application. Suppose a team of software engineers judged 35,000 DSI as a reasonable assessment of the 50th percentile of I and a size of 60,000 DSI as a reasonable assessment of the 95th percentile. Furthermore, suppose the distribution function below is a good characteristization of the distribution of the uncertainty in the number of DSI. (See Example 4.11, page 118 for a similar problem). Given this: a. Find the extreme possible values for I. b. Compute the mode of 1. c. Compute E(I) and o d. Compute P(1 ≤45,000) e. Compute P(1 ≤x) = 0.50 fix) ase 1-Beta (2, 3.5, a, b) Xass DSI b

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
Preliminary information:
A random variable X is said to have a beta distribution if its PDF is given by:
1
fx (x) = b-a
X~Beta(a. B.a, b)
A random variable Y is said to have a standard beta distribution if its PDF is given by:
The mode of Y is given by:
α-1
B-1
² ( ² = 2 ) *¹ (ta) ³-¹
r(x+B)(x-a
Γ(α)Γ(β)
fy(y) =r(a)r (B)
Y~Beta(a, B)
One may transform from X~Beta(a, ß, a, b) to Y~Beta(a, ß) by letting y = (x-a)/(b-a) which means that x =a +
(ba) -y. The expected values and variances for the beta distribution and standard beta distribution are:
Για + β) (y)-1(1-y)B-1 0 <y < 1
otherwise
a. Find the extreme possible values for I.
b. Compute the mode of I.
c. Compute E(I) and σ,
d. Compute P(1 ≤ 45,000)
e. Compute P(1 ≤x) = 0.50
X
a + B
E(X) = a + (b-a)E(Y)
E(Y) =
Var(Y) =
aß
(a + B + 1)(a +B)²
Var(X)= (ba)² Var(Y)
1-a
y=2-a-B
With a and B and any two fractiles x; and x;, the minimum and maximum possible values of X are given by the below:
a=
xjxjyi
Yj-yi
b = x (1-yi) -xi (1-yj)
y₁ - y
Suppose I represents the uncertainty in the number of Delivered Source Instructions (DSI) for a new software application.
Suppose a team of software engineers judged 35,000 DSI as a reasonable assessment of the 50th percentile of I and a size
of 60,000 DSI as a reasonable assessment of the 95th percentile. Furthermore, suppose the distribution function below is a
good characteristization of the distribution of the uncertainty in the number of DSI. (See Example 4.11, page 118 for a
similar problem).
Given this:
a<x<b
otherwise
fix)
a
0.50
I-Beta (2, 3.5, a, b)
X0.95
DSI
b
*
Transcribed Image Text:Preliminary information: A random variable X is said to have a beta distribution if its PDF is given by: 1 fx (x) = b-a X~Beta(a. B.a, b) A random variable Y is said to have a standard beta distribution if its PDF is given by: The mode of Y is given by: α-1 B-1 ² ( ² = 2 ) *¹ (ta) ³-¹ r(x+B)(x-a Γ(α)Γ(β) fy(y) =r(a)r (B) Y~Beta(a, B) One may transform from X~Beta(a, ß, a, b) to Y~Beta(a, ß) by letting y = (x-a)/(b-a) which means that x =a + (ba) -y. The expected values and variances for the beta distribution and standard beta distribution are: Για + β) (y)-1(1-y)B-1 0 <y < 1 otherwise a. Find the extreme possible values for I. b. Compute the mode of I. c. Compute E(I) and σ, d. Compute P(1 ≤ 45,000) e. Compute P(1 ≤x) = 0.50 X a + B E(X) = a + (b-a)E(Y) E(Y) = Var(Y) = aß (a + B + 1)(a +B)² Var(X)= (ba)² Var(Y) 1-a y=2-a-B With a and B and any two fractiles x; and x;, the minimum and maximum possible values of X are given by the below: a= xjxjyi Yj-yi b = x (1-yi) -xi (1-yj) y₁ - y Suppose I represents the uncertainty in the number of Delivered Source Instructions (DSI) for a new software application. Suppose a team of software engineers judged 35,000 DSI as a reasonable assessment of the 50th percentile of I and a size of 60,000 DSI as a reasonable assessment of the 95th percentile. Furthermore, suppose the distribution function below is a good characteristization of the distribution of the uncertainty in the number of DSI. (See Example 4.11, page 118 for a similar problem). Given this: a<x<b otherwise fix) a 0.50 I-Beta (2, 3.5, a, b) X0.95 DSI b *
Expert Solution
steps

Step by step

Solved in 5 steps with 31 images

Blurred answer
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman