Drw Statistics & Math Interview Questions
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Compute expected arc length on a circle
On the unit circle (radius \(1\), centered at the origin), pick three points independently and uniformly at random on the circumference. These three p...
Analyze distribution of a 3-dice product
You roll three independent fair 10-sided dice. Each die shows an integer in \(\{0,1,\dots,9\}\) with equal probability. Let the outcomes be \(X,Y,Z\),...
Differentiate sample vs population standard deviation
Population vs. Sample Standard Deviation in a Finite Rolling Window Context You are implementing a rolling standard deviation over a fixed-size window...
Solve Markov and distribution expectation problems
Statistics, Linear Algebra, and Game Theory Fundamentals 1) Stationary Distribution of a Finite Markov Chain Given a finite Markov chain with transiti...
Compute Markov steady state and expectations
Probability and Game Theory: Three Sub-questions Context: The exact transition matrix P (for Q1) and the 2×2 payoff matrix (for Q3) are not provided. ...
Derive eigenvalues and sum for inverse matrix
Eigenvalues of an Inverse and Their Sum Context Let A be an invertible n×n matrix (over the real or complex numbers). All eigenvalues of A are nonzero...