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**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?