The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. f(x) = {0.075x + (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 1 0.07 0.075x + 0.2 dx = 0.2 (b) Calculate P(X ≤ 4). 2 3 ≤x≤ 5 otherwise 3 2 3 = 1.9375 - 4 5 4 5 5 X X f(x) 0.6 0.5 Verify that the total area under the density curve is indeed 1. 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. f(x) = {0.075x + (a) Graph the pdf. f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O f(x) 0.6 0.5 0.4 0.3 0.2 0.1 O 1 1 0.07 0.075x + 0.2 dx = 0.2 (b) Calculate P(X ≤ 4). 2 3 ≤x≤ 5 otherwise 3 2 3 = 1.9375 - 4 5 4 5 5 X X f(x) 0.6 0.5 Verify that the total area under the density curve is indeed 1. 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
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Please solve a, b, and c.
![The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function.
Jo.075x + 0.2
(a) Graph the pdf.
f(x)
0.6
0.5
0.4
0.3
0.2
0.1
f(x)
0.6
0.5
0.4
0.3
f(x)
0.2
0.1
5
1
1
0.075x + 0.2 dx =
2
(b) Calculate P(X ≤ 4).
2
3 ≤ x ≤ 5
otherwise
= 1.9375
3
3
4
5
3
4
5
X
Verify that the total area under the density curve is indeed 1.
X
f(x)
0.6
0.5
0.4
0.3
0.2
0.1
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7afdb6c4-3a61-4c47-91da-dfd2e9ec1a67%2F49c5e4c7-d249-480a-8289-e5693bc6036c%2Fh35kvxs_processed.png&w=3840&q=75)
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.
Jo.075x + 0.2
(a) Graph the pdf.
f(x)
0.6
0.5
0.4
0.3
0.2
0.1
f(x)
0.6
0.5
0.4
0.3
f(x)
0.2
0.1
5
1
1
0.075x + 0.2 dx =
2
(b) Calculate P(X ≤ 4).
2
3 ≤ x ≤ 5
otherwise
= 1.9375
3
3
4
5
3
4
5
X
Verify that the total area under the density curve is indeed 1.
X
f(x)
0.6
0.5
0.4
0.3
0.2
0.1
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
![(b) Calculate P(X ≤ 4).
How does this probability compare to P(X < 4)?
O P(X ≤ 4) < P(X < 4)
P(X ≤ 4) > P(X < 4)
P(X ≤ 4) = P(X < 4)
(c) Calculate P(3.5 ≤ X ≤ 4.5).
Calculate P(4.5 < X).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7afdb6c4-3a61-4c47-91da-dfd2e9ec1a67%2F49c5e4c7-d249-480a-8289-e5693bc6036c%2Fuqyge9d_processed.png&w=3840&q=75)
Transcribed Image Text:(b) Calculate P(X ≤ 4).
How does this probability compare to P(X < 4)?
O P(X ≤ 4) < P(X < 4)
P(X ≤ 4) > P(X < 4)
P(X ≤ 4) = P(X < 4)
(c) Calculate P(3.5 ≤ X ≤ 4.5).
Calculate P(4.5 < X).
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