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We have a set $X_1, X_2$, . . . , $X_n$ iid standard normal random variables. How would I go about finding $P(X_n \ge max(X_1, X_2, \dots , X_{n-1}))$

Vimal
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pluto
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    Welcome to CV. Since you’re new here, you may want to take our tour, which has information for new users. Since this looks like homework (apologies if it's not), please add the [self-study] tag and read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. Please make these changes as just posting your homework & hoping someone will do it for you is grounds for closing. If this is self-study rather than homework, let us know, and... it's still a good idea to show us what you've tried. – jbowman May 03 '20 at 01:28
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    In random sampling from any continuous distribution, the probability that the last of $n$ randomly chosen observations will be their maximum is $1/n.$ // Your question is not exactly clear to me, so that may not be what you're asking. – BruceET May 03 '20 at 03:18
  • Also answered at https://stats.stackexchange.com/q/133616/119261. – StubbornAtom May 03 '20 at 21:04

1 Answers1

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The event $X_n \geqslant \max(X_1,...,X_{n-1})$ is equivalent to $X_n = \max (X_1,...,X_n)$ so you are really just asking for the probability that the $n$th sample value is the maximum. You have two conditions to get this: the first is that the values are IID, and the second is that they come from a continuous distribution. Think about what each of these things implies, and you should be able to find the resulting probability (which is extremely simple).

Ben
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