TASK 1: INTEGRATION Another application of integration is in probability. This task applies your algebra and calculus skills to this domain. If X is a continuous random variable with range [a, b] then the probability density function satisfies the following two properties: Property 1: f(x) ≥ 0 for all x € [a, b]. Property 2: [s a f(x) dx = 1. Question 1 (1) Explain why the following functions are, or are not, probability density functions: (a) f(x) = ² for x = [1, √e] (b) f(x) = 5 (9x² - x4) for x = [0, 3] 1
TASK 1: INTEGRATION Another application of integration is in probability. This task applies your algebra and calculus skills to this domain. If X is a continuous random variable with range [a, b] then the probability density function satisfies the following two properties: Property 1: f(x) ≥ 0 for all x € [a, b]. Property 2: [s a f(x) dx = 1. Question 1 (1) Explain why the following functions are, or are not, probability density functions: (a) f(x) = ² for x = [1, √e] (b) f(x) = 5 (9x² - x4) for x = [0, 3] 1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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show that propery 1 and 2 holds
![TASK 1: INTEGRATION
Another application of integration is in probability. This task applies your algebra
and calculus skills to this domain.
If X is a continuous random variable with range [a, b] then the probability density
function satisfies the following two properties:
Property 1: f(x) ≥ 0 for all x € [a, b].
Property 2:
2: [". f(x) dx = 1.
a
Question 1
(1) Explain why the following functions are, or are not, probability density functions:
(a) f(x) = for x = [1, √e]
I
(b) f(x) = 5 (9x²-x4) for x = [0,3]
1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6954de0d-2b65-4359-813b-d12332619368%2Fbc3a5f30-f37d-49ee-9aa8-f659013409aa%2Fz68rhco_processed.png&w=3840&q=75)
Transcribed Image Text:TASK 1: INTEGRATION
Another application of integration is in probability. This task applies your algebra
and calculus skills to this domain.
If X is a continuous random variable with range [a, b] then the probability density
function satisfies the following two properties:
Property 1: f(x) ≥ 0 for all x € [a, b].
Property 2:
2: [". f(x) dx = 1.
a
Question 1
(1) Explain why the following functions are, or are not, probability density functions:
(a) f(x) = for x = [1, √e]
I
(b) f(x) = 5 (9x²-x4) for x = [0,3]
1
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