Interview Question 2: Central Limit Theorem

1 Q: Roll 100 dice together, what is the probability that the sum of all dice is 400? A Central Limit Theorem: Let \(X_1, X_2,... X_n\) be independent and identically distributed random variables. The sum of these random variables approaches a normal distribution as \(n \rightarrow \infty\) $$ \sum_{i=1}^n X_i \sim N(n \cdot \mu, n \cdot \sigma^2) $$ , where \(\mu = E[X_i]\) and \(\sigma^2 = Var(X_i)\). Let \(X\) be the value of a die.

Read More

Interview Question 1: Expectations

1 Given a deck of 52 cards, only consider the color black and red. Shuffle the cards. Define that a group is a sequence of same-color cards. For example, Red/Black/Black/Black/Red/Red is an array of 3 groups. Q: What is the expected number of groups? A: Consider a simple case of 2 cards. If they have the same color, the \(E\) will be 1. \(E\) will be 2 if the 2 cards have different colors.

Read More

ML Note: Entropy

#the-canvas { border: 1px solid black; direction: ltr; width: 100%; height: auto; } #paginator{ text-align: center; margin-bottom: 10px; } Previous Next     Page: / window.onload = function() { var url = "\/files\/Entropy_Cross_Entropy_and_KL_Divergence_Brief_Review.pdf"; var pdfjsLib = window['pdfjs-dist/build/pdf']; pdfjsLib.GlobalWorkerOptions.workerSrc = '/js/pdf-js/build/pdf.worker.js'; var pdfDoc = null, pageNum = 1, pageRendering = false, pageNumPending = null, scale = 3, canvas = document.getElementById('the-canvas'), ctx = canvas.getContext('2d'); function renderPage(num) { pageRendering = true; pdfDoc.

Read More

ML Note: Regularization

#the-canvas { border: 1px solid black; direction: ltr; width: 100%; height: auto; } #paginator{ text-align: center; margin-bottom: 10px; } Previous Next     Page: / window.onload = function() { var url = "\/files\/Regularization_Note.pdf"; var pdfjsLib = window['pdfjs-dist/build/pdf']; pdfjsLib.GlobalWorkerOptions.workerSrc = '/js/pdf-js/build/pdf.worker.js'; var pdfDoc = null, pageNum = 1, pageRendering = false, pageNumPending = null, scale = 3, canvas = document.getElementById('the-canvas'), ctx = canvas.getContext('2d'); function renderPage(num) { pageRendering = true; pdfDoc.

Read More