Solution Found!
Solved: Let Y1, Y2, . . . , Yn be independent,
Chapter 6, Problem 86E(choose chapter or problem)
Problem 86E
Let Y1, Y2, . . . , Yn be independent, exponentially distributed random variables with mean β. Give the
a density function for Y(k), the kth-order statistic, where k is an integer between 1 and n.
b joint density function for Y( j ) and Y(k) where j and k are integers 1 ≤ j < k ≤ n.
Questions & Answers
QUESTION:
Problem 86E
Let Y1, Y2, . . . , Yn be independent, exponentially distributed random variables with mean β. Give the
a density function for Y(k), the kth-order statistic, where k is an integer between 1 and n.
b joint density function for Y( j ) and Y(k) where j and k are integers 1 ≤ j < k ≤ n.
ANSWER:
Step 1 of 5
Let be independent, exponentially distributed random variables with mean
The common density function of with mean is:
Now the cumulative distribution is calculated as: