Identify binomial model and compute moments
Company: Upstart
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: HR Screen
You toss N independent balls toward a cup; each ball lands in the cup with probability p, 0<p<1. Let K be the number of balls in the cup. a) What is the distribution of K? b) Write its pmf P(K=k). c) Compute E[K] and Var(K). d) Briefly state how your answers would change if tosses were dependent or if p varied by ball.
Quick Answer: This question evaluates understanding of probability distributions and independence by identifying the binomial model and computing its probability mass function, expectation, and variance, assessing core probabilistic competency for data scientist roles.