6
votes
$X,Y$ are iid from $N(0,1)$. Compute the probability of $X > Y > 0$
Think about the joint distribution of $x,y$ as a sphericallly symmetric distribution.
Then consider which region relates to the condition $X>Y>0$ and the question becomes as easy as slicing ...
- 71.9k
5
votes
$X,Y$ are iid from $N(0,1)$. Compute the probability of $X > Y > 0$
You don't need to bring "conditional probability" concept (the "independence" condition can be utilized to circumvent any conditioning argument) in to solve this question. In ...
- 16.8k
4
votes
Accepted
Expectation of product of sample averages
Even in very advanced mathematics it helps to study simple examples. Part of the art of reading and learning mathematics is to construct such examples for yourself. This answer illustrates the ...
- 316k
2
votes
How many times do I need to toss to differentiate between two biased coins?
As @PBulls points out in a comment, this quote from the video is probably a very informal summary of some probabilistic bound on $|\hat p - p|$.
One simple example of how to approach this is to use ...
- 3,462
2
votes
Does the likelihood of getting a certain person in secret santa decrease if you were going first versus going last, and how much?
Prior probabilities
There is one problem with the algorithm: it is possible that the last person will draw their own name, in which case they can't put it back and draw another name.
One simple way to ...
- 466
2
votes
Accepted
Statistics Inference Question: "Prob(An equation) = 1" compared with "The equation holds"
The concept you are looking for is almost surely: suppose in the probability space $(\Omega,\boldsymbol{\mathfrak A},\Pr),$ we are investigating to see whether a property $P$ holds.
Now what we ...
- 6,992
2
votes
Accepted
Question on basic probability conditioning
Using the observation that you have made (i.e., the De Morgan law and the complementary law) shows that it is equivalent to prove
\begin{align*}
P(A \cup B) \leq P(A \cup B|D). \tag{1}\label{1}
\end{...
- 16.8k
1
vote
Accepted
what is the difference between these two expressions
Usually none, since you can simply flip the sign on your coefficient.
There is a difference of course if during model fitting you constrain your parameter to be (say) nonnegative. Or if you regularize ...
- 118k
1
vote
Is this a typo on P.75, Theorem 5.52 of the book "Asymptotic Statistics" by Van der Vaart?
First point: Since $d(\theta, \theta_0)<\delta$ it should be possible to select $\theta = \theta_0$ which gives $\sup=0>-C\cdot0^\alpha$.
Without being specific for this problem, if $x^*=\arg\...
- 1,843
1
vote
What is the probability of selecting couples from a waiting room?
In this solution $N$ is the number of couples, and $N=2h$, where $h$ is the half-number. The number $k$ represents how many matching pairs we want, and $n$ is the number of people called.
It would be ...
- 2,186
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