Homework SourseA random variable X is exponentially distributed with a mean
A random variable X is exponentially distributed with a mean of 0.16.
| a-1. | What is the rate parameter ? (Round your answer to 3 decimal places.) |
Solution
a-1.
lambda = 1/mean = 1/0.16 = 6.25 [answer]
a-2.
standard deviation = mean = 0.16 [answer]
b)
The mean of the distirbution is also the standard deviation, and is equal to 1/lambda:
mean = standard deviation = 1/lambda = 0.16
The area between two values in an exponential distribution ois
Area = e^(-lambda*x)
As
x = critical value = 0.24
Then
Area = 0.22313016 [ANSWER]
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C)
The mean of the distirbution is also the standard deviation, and is equal to 1/lambda:
mean = standard deviation = 1/lambda = 0.16
The area between two values in an exponential distribution ois
Area = e^(-lambda*x2) - e^(-lambda*x1)
As
x1 = lower bound = 0.09
x2 = upper bound = 0.24
Then
Area = 0.346652665 [answer]
