Question 2 • Find the probability P(x ≤ 3) given the probability density function you identi- fied in Question 1. Give an exact answer, and an approximate answer to two decimal places. • Why is Property 1 in Question (1) essential for a function to be a probability density function?
Question 2 • Find the probability P(x ≤ 3) given the probability density function you identi- fied in Question 1. Give an exact answer, and an approximate answer to two decimal places. • Why is Property 1 in Question (1) essential for a function to be a probability density function?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
Related questions
Question
please answer question 2
![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:
TASK 1: INTEGRATION
b
[² f
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 — xª) for x = [0, 3]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6954de0d-2b65-4359-813b-d12332619368%2Fdd9286b3-bb56-4288-b3dd-d05ba1d20052%2F7ky1ng_processed.png&w=3840&q=75)
Transcribed Image Text: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:
TASK 1: INTEGRATION
b
[² f
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 — xª) for x = [0, 3]
![Given a probability density function f(x) with range [a, b], we can obtain the
probability that X is at most k
from the area of a region under the function.
P(X ≤ k) = f* f(x)dx
a
To find the probability that c≤ x ≤k:
rk
P(c ≤ x ≤ k) = √ k f(x)dx
Note: P(X <k) = P(X ≤ k).
Question 2
• Find the probability P(x ≤ 3) given the probability density function you identi-
fied in Question 1.
Give an exact answer, and an approximate answer to two decimal places.
• Why is Property 1 in Question (1) essential for a function to be a probability
density function?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6954de0d-2b65-4359-813b-d12332619368%2Fdd9286b3-bb56-4288-b3dd-d05ba1d20052%2Fleaiy95_processed.png&w=3840&q=75)
Transcribed Image Text:Given a probability density function f(x) with range [a, b], we can obtain the
probability that X is at most k
from the area of a region under the function.
P(X ≤ k) = f* f(x)dx
a
To find the probability that c≤ x ≤k:
rk
P(c ≤ x ≤ k) = √ k f(x)dx
Note: P(X <k) = P(X ≤ k).
Question 2
• Find the probability P(x ≤ 3) given the probability density function you identi-
fied in Question 1.
Give an exact answer, and an approximate answer to two decimal places.
• Why is Property 1 in Question (1) essential for a function to be a probability
density function?
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