Suppose that X is a random variable with probability density function fx(x) and cumulative distribution function fx(x). Additionally, suppose X can only take on positive values; that is, P(X > 0) = 1. Show that the following equality holds: ro 8 [1 - Ex(x)]dx = tfx(t)dt Hint: Write [1 Fx (x)] as an integral of fr(t) to get a double integral on the left-hand side. Then, switch the order of integration.
Suppose that X is a random variable with probability density function fx(x) and cumulative distribution function fx(x). Additionally, suppose X can only take on positive values; that is, P(X > 0) = 1. Show that the following equality holds: ro 8 [1 - Ex(x)]dx = tfx(t)dt Hint: Write [1 Fx (x)] as an integral of fr(t) to get a double integral on the left-hand side. Then, switch the order of integration.
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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![Suppose that X is a random variable with probability density function fx(x) and cumulative
distribution function fx(x). Additionally, suppose X can only take on positive values; that is,
P(X > 0) = 1. Show that the following equality holds:
[1 - Ex(x)]dx = f* tfx(t)dt
Hint: Write [1 – Fx (x)] as an integral of fr(t) to get a double integral on the left-hand side.
Then, switch the order of integration.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccac55ee-732b-4607-a38e-f5bd0a8aacb2%2F4cb35731-68d1-4b9f-b2c6-76d6c17ed5c3%2Fhewhbx_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose that X is a random variable with probability density function fx(x) and cumulative
distribution function fx(x). Additionally, suppose X can only take on positive values; that is,
P(X > 0) = 1. Show that the following equality holds:
[1 - Ex(x)]dx = f* tfx(t)dt
Hint: Write [1 – Fx (x)] as an integral of fr(t) to get a double integral on the left-hand side.
Then, switch the order of integration.
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