The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. [0.025x + 0.4 f(x) = 0 3≤x≤5 otherwise (a) Graph the pdf. f(x) f(x) f(x) 1 2 O 3 4 5 3 O Verify that the total area under the density curve is indeed 1. 0.0 0.025x + 0.4 dx = = 2.3125 - (b) Calculate P(X ≤ 4). How does this probability compare to P(X < 4)? O P(X ≤ 4) = P(X < 4) O P(X ≤ 4) > P(X <4) O P(X ≤ 4) < P(X < 4) (c) Calculate P(3.5 ≤ x ≤ 4.5). Calculate P(4.5 < X). 0.6 0.5 0.4 0.3 0.2 0.1 X 0.6 0.5 0.4 0.3 0.2 0.1 1 2 4 0.6 0.5 0.4 0.3 0.2 0.1 O 1 2 3 4 5 X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 2 3 4 5 X
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. [0.025x + 0.4 f(x) = 0 3≤x≤5 otherwise (a) Graph the pdf. f(x) f(x) f(x) 1 2 O 3 4 5 3 O Verify that the total area under the density curve is indeed 1. 0.0 0.025x + 0.4 dx = = 2.3125 - (b) Calculate P(X ≤ 4). How does this probability compare to P(X < 4)? O P(X ≤ 4) = P(X < 4) O P(X ≤ 4) > P(X <4) O P(X ≤ 4) < P(X < 4) (c) Calculate P(3.5 ≤ x ≤ 4.5). Calculate P(4.5 < X). 0.6 0.5 0.4 0.3 0.2 0.1 X 0.6 0.5 0.4 0.3 0.2 0.1 1 2 4 0.6 0.5 0.4 0.3 0.2 0.1 O 1 2 3 4 5 X f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 2 3 4 5 X
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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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.
(0.025x + 0.4
f(x) =
3 ≤x≤ 5
otherwise
0
(a) Graph the pdf.
f(x)
f(x)
f(x)
0.6
0.5
0.4
0.3
0.2
0.1
3
0.6
0.5
0.4
0.3
0.2
0.1
X
O
1 2
3 4 5
Verify that the total area under the density curve is indeed 1.
5
5
[³
0.025x + 0.4 dx =
= 2.3125 -
(b) Calculate P(X ≤ 4).
How does this probability compare to P(X < 4)?
O P(X ≤ 4) = P(X < 4)
O P(X ≤4) > P(X < 4)
O P(X ≤ 4) < P(X < 4)
(c) Calculate P(3.5 ≤ x ≤ 4.5).
Calculate P(4.5 < X).
1 2
4
5
0.6
0.5
0.4
0.3
0.2
0.1
O
1 2 3
4
5
X
f(x)
0.6
0.5
0.4
0.3
0.2
0.1
1 2 3
4
5
X
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