While playing a friendly game of Texas Hold'em poker, a player drew a 7 card straight. Although in texas hold'em a player may only use 5 of the possible 7 cards, the discussion about odds immediately came up. What are the odds of getting a 7 card straight? For those unfamiliar with poker, the question … Read more
I'm trying to generate many draws (i.e., realizations) of a Gaussian process $e_i(t)$, $1leq t leq T$ with mean 0 and covariance function $gamma(s,t)=exp(-|t-s|)$. Is there an efficient way to do this that wouldn't involve computing the square root of a $T times T$ covariance matrix? Alternatively can anyone recommend an R package to do … Read more
So I always thought of the Student t-distribution as having only 1 parameter, v, the degrees of freedom (as described by wikipedia). When I searched however on how to find the MLE of v I keep coming across questions mentioning mu and sigma as parameters as well. So 1) Is the Student-t Distribution a special … Read more
This question stems from a children's board game where if you succeed in flipping all heads after three attempts you can perform the desired action, and if not then your opponent gets to perform their desired action. Now for the problem: Flip three coins. If you get any heads, set them aside and flip the … Read more
I have detector which will detect an event with some probability p. If the detector says that an event occured, then that is always the case, so there are not false-positives. After I run it for some time, I get k events detected. I would like to calculate what the total number of events that … Read more
I have detector which will detect an event with some probability p. If the detector says that an event occured, then that is always the case, so there are not false-positives. After I run it for some time, I get k events detected. I would like to calculate what the total number of events that … Read more
What's the reasoning for checking the independence of $$min(X,Y)$$ and $$max(X,Y)$$ for independent r.v.s $X,Y$? Is it possible that $min$ and $max$ both select the same r.v. in which case they would be dependent? No, because that would mean that $X=Y$, i.e. $X$ and $Y$ would not be independent. Does the independence regarding functions of … Read more
What's the reasoning for checking the independence of $$min(X,Y)$$ and $$max(X,Y)$$ for independent r.v.s $X,Y$? Is it possible that $min$ and $max$ both select the same r.v. in which case they would be dependent? No, because that would mean that $X=Y$, i.e. $X$ and $Y$ would not be independent. Does the independence regarding functions of … Read more
It is well know that integrating a probability density function gives probability, that is, $$P(Xgeq a) = int_a^infty f_X(x), dx$$ where $X$ is a continuous random variable, $a$ is a scalar and $f_X(x)$ is the probability density function of $X.$ Question: Why is this the case? When I learn this, I just memorize this without … Read more
It is well know that integrating a probability density function gives probability, that is, $$P(Xgeq a) = int_a^infty f_X(x), dx$$ where $X$ is a continuous random variable, $a$ is a scalar and $f_X(x)$ is the probability density function of $X.$ Question: Why is this the case? When I learn this, I just memorize this without … Read more