The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. f(x) = {0.07 (0.075x + 0.2 3 ≤ x ≤ 5 0 otherwise (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 X 2 3 4 5 f(x) 0.6 0.5 0.4F 0.3 0.2 0.1 Verify that the total area under the density curve is indeed 1. 5 0.075x + 0.2 dx = (b) Calculate P(X ≤ 4). (c) 5 3 = 1.9375 - How does this probability compare to P(X < 4)? ○ P(X ≤ 4) > P(X < 4) P(X ≤ 4) < P(X < 4) P(X ≤ 4) = P(X < 4) Calculate P(3.5 ≤ X ≤ 4.5). Calculate P(4.5
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. f(x) = {0.07 (0.075x + 0.2 3 ≤ x ≤ 5 0 otherwise (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 X 2 3 4 5 f(x) 0.6 0.5 0.4F 0.3 0.2 0.1 Verify that the total area under the density curve is indeed 1. 5 0.075x + 0.2 dx = (b) Calculate P(X ≤ 4). (c) 5 3 = 1.9375 - How does this probability compare to P(X < 4)? ○ P(X ≤ 4) > P(X < 4) P(X ≤ 4) < P(X < 4) P(X ≤ 4) = P(X < 4) Calculate P(3.5 ≤ X ≤ 4.5). Calculate P(4.5
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.4: Logarithmic Functions
Problem 45E
Related questions
Question
Transcribed Image Text:The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function.
f(x)
=
{0.07
(0.075x + 0.2
3 ≤ x ≤ 5
0
otherwise
(a) Graph the pdf.
f(x)
0.6
0.5
0.4
0.3
0.2
0.1
X
2
3
4
5
f(x)
0.6
0.5
0.4F
0.3
0.2
0.1
Verify that the total area under the density curve is indeed 1.
5
0.075x + 0.2 dx =
(b) Calculate P(X ≤ 4).
(c)
5
3
= 1.9375 -
How does this probability compare to P(X < 4)?
○ P(X ≤ 4) > P(X < 4)
P(X ≤ 4) < P(X < 4)
P(X ≤ 4) = P(X < 4)
Calculate P(3.5 ≤ X ≤ 4.5).
Calculate P(4.5 <X).
1
2
3
4
f(x)
f(x)
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
x
1
2
3
4
5
X
1
2
3
4
5
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
