• Support PF! Buy your school textbooks, materials and every day products Here!

A Probability Problem Involving 6 Random Variables

  • Thread starter e(ho0n3
  • Start date
  • #1
1,357
0
Homework Statement
Let [itex]X_1, \ldots, X_6[/itex] be a sequence of independent and identically distributed continuous random variables. Find

(a) [itex]P\{X_6 > X_1 \, | \, X_1= \max(X_1, \ldots, X_5)\}[/itex]
(b) [itex]P\{X_6 > X_2 \, | \, X_1 = \max(X_1, \ldots, X_5)\}[/itex]

The attempt at a solution
(a) is the probability that [itex]X_6 = \max(X_1, \ldots, X_6)[/itex] right? How would I determine this probability? In (b), the event [itex]X_6 > X_2[/itex] is independent of [itex]X_1 = \max(X_1, \ldots, X_5)[/itex] right? If it is, the probability is:

[tex]\int_{-\infty}^{\infty} \int_{x_1}^{\infty} f(x_6, x_1), \, dx_6 \, dx_1[/itex]

where [itex]f(x_6, x_1) = f(x_6)f(x_1)[/itex] since the random variables are independent. Right?
 

Answers and Replies

  • #2
1,357
0
[tex]\int_{-\infty}^{\infty} \int_{x_1}^{\infty} f(x_6, x_1), \, dx_6 \, dx_1[/itex]

where [itex]f(x_6, x_1) = f(x_6)f(x_1)[/itex] since the random variables are independent. Right?
I screwed up. [itex]x_1[/itex] should be [itex]x_2[/itex] in the above.
 

Related Threads for: A Probability Problem Involving 6 Random Variables

Replies
7
Views
1K
Replies
3
Views
2K
Replies
4
Views
4K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
3K
Top