Compute the Median for the exponential distribution with parameter λ:
2025
Compute the Median for the exponential distribution with parameter λ:
- A.
log(3)/λ
- B.
log(2)/2λ
- C.
2log(2)/λ
- D.
log(2)/λ
Attempted by 6 students.
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Correct answer: D
Step-by-Step Solution
To find the median (m) of a continuous probability distribution, we must find the value where the Cumulative Distribution Function (CDF) equals 0.5.
Identify the CDF: For an exponential distribution with parameter λ, the CDF is:
F(x) = 1 - e^(-λx)
Set the CDF to 0.5: To find the median (m), we solve:
1 - e^(-λm) = 0.5
Rearrange the equation:
e^(-λm) = 1 - 0.5
e^(-λm) = 0.5
Take the natural logarithm (log) of both sides:
-λm = log(0.5)
Simplify:
Since log(0.5) is the same as -log(2):
-λm = -log(2)
m = log(2) / λ