The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following density function. So.075x + 0.2 f(x) 3 P(X < 4) O P(X S 4) < P(X < 4) (c) Calculate P(3.5 SX< 4.5). Calculate P(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. So.075x + 0.2 f(x) 3 P(X < 4) O P(X S 4) < P(X < 4) (c) Calculate P(3.5 SX< 4.5). Calculate P(4.5 < X).
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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.
So.075x + 0.2
f(x)
3 <x<5
=
otherwise
(a) Graph the pdf.
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
1.
2
3 4
5
1.
2
3
4
f(x)
f(x)
0.6
0.6
0.5E
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
X
X
1
2
3
4
5
1
3
4
Verify that the total area under the density curve is indeed 1.
'5
0.075x + 0.2 dx =
/3
3
= 1.9375
(b) Calculate P(X < 4).
How does this probability compare to P(X < 4)?
O P(X S 4) = P(X < 4)
O P(X S 4) > P(X < 4)
O P(X S 4) < P(X < 4)
(c) Calculate P(3.5 SX< 4.5).
Calculate P(4.5 < X).
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