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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

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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 *
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