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Chapter 8: Q 8.1 (page 390)

Suppose that X is a random variable with mean and variance both equal to 20. What can be said about P{0 < X < 40}?

Short Answer

Expert verified

P[0<X<40]鈮�1920

Step by step solution

01

Step 1. Given information

Let X is a random variable with mean and variance both 20.

02

Step 2. Denoting mean and variance

E(X) = 20

V(X) = 20

03

Step 3. To find

P[0<X<40]

04

Step 4. Simplification

P[0-20<X-20<40-20]=P[-20<X-20<20]=P[|X-20|<20]

05

Step 5. Using Chebyshev's inequality

1-P[|X-20|鈮�20]鈮�1-120=1920

06

Step 6. Final answer 

P[0<X<40]鈮�1920

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