Using the uniform probability density function shown in Figure 5.7, find the probability that the random variable X is between 1.4 and 1.8.

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  1. Using the uniform probability density function shown in Figure 5.7, find the probability that the random variable X is between 1.4 and 1.8.

Figure 5.7 Probability Density Function for Example 5.1
f(x)
.5
0
0
xo
2 x
The probability that a fracture occurs between 0.5 mile and 1.5 miles along the pipe is
as follows:
P(0.5 < X < 1.5) = F(1.5) – F(0.5) = (0.5)(1.5) - (0.5)(0.5) = 0.5
This is the area under the probability density function from x = 0.5 to x = 1.5.
Transcribed Image Text:Figure 5.7 Probability Density Function for Example 5.1 f(x) .5 0 0 xo 2 x The probability that a fracture occurs between 0.5 mile and 1.5 miles along the pipe is as follows: P(0.5 < X < 1.5) = F(1.5) – F(0.5) = (0.5)(1.5) - (0.5)(0.5) = 0.5 This is the area under the probability density function from x = 0.5 to x = 1.5.
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