4 posts on probability. All posts · RSS feed
The last episode of 3Blue1Brown's "lockdown math" series posed the problem: given two numbers, and , chosen randomly from the uniform distribution between 0 and 1, what is the proportion that their ratio, when rounded down to the nearest integer, is even? That is, what …
Bertrand's Paradox is an illustration of the need to define the mechanism for picking a random variable carefully for its associated probability to be well-defined. Consider an equilateral triangle inscribed in a circle. What is the probability that a randomly-chosen chord of the circle is …
Suppose a fair coin is tossed times and the number of "heads", , and "tails", , recorded after each toss. Over the course of the trial, how many times is the number of heads recorded greater than the number of tails? Naive intuition might lead …
The multivariate Gaussian distribution of an -dimensional vector may be written where is the -dimensional mean vector and is the covariance matrix. To visualize the magnitude of as a function of all the dimensions requires a plot in dimensions, so visualizing this distribution for is …
