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Chapter 6: Q6.17 (page 272)

Three points X1, X2, X3 are selected at random on a line L. What is the probability that X2 lies between X1 and X3?

Short Answer

Expert verified

The probability that X2 lies between X1 and X3 is13

Step by step solution

01

Content Introduction 

Three points X1 , X2 , X3 are selected at a random on a line L.

Number of ways of arranging and things taking all at a time is n!. Total number of points is 3.

So, the number of ways of arranging 3 points on a line is 3! which is equal to 6.

02

Content Explanation

Possible arrangements are:

X1X2X3X1X3X2X2X1X3X2X3X1X3X1X2X3X1X2

Out of these X2 lies between X1 and X3in two arrangements.

Therefore, Probability that X2lies between X1and X3is=26=13

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Most popular questions from this chapter

The random variables XandYhave joint density function f(x,y)=12xy(1鈭�x)0<x<1,0<y<1and equal to0 otherwise.

(a) Are XandYindependent?

(b) Find E[X].

(c) FindE[Y].

(d) Find Var(X).

(e) Find Var(Y).

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(b) Find the density function of X.

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The joint density of X and Y is

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