In: Statistics and Probability
A random variable X is exponentially distributed with
an expected value of 50.
a-1. What is the rate parameter λ?
(Round your answer to 3 decimal places.)
a-2. What is the standard deviation of
X?
b. Compute P(44 ≤ X ≤ 56).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
c. Compute P(36 ≤ X ≤ 64).
(Round intermediate calculations to at least 4 decimal
places and final answer to 4 decimal places.)
a-1
The parameter of an exponential distribution is given as
Where is the expected value
Hence
a-2
Standard deviation is the same as the expected value of X i.e. 50
a-3
We need to compute . Therefore, the following is obtained:
a-4
We need to compute Pr(36≤X≤64). Therefore, the following is obtained:
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