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lect04, Thu 04/09

Pandas

Announcements

• HW 1 due tomorrow

• HW 2 out tomorrow (due in 2 weeks)

Probability Distribution

Concrete: n = 4 and Y = X1 + X2 + X3 + X4 and the Xs are independent with same chance of 0 or 1 (knowing the value of X1 doesn’t change X2 distribution). P(Y = 2) =

n independent 0-1 variables

Y = X1 + … + Xn

P(Xi = 1) = p

Probability Mass Function

Probability Problem Related to

question on HW 2:

• Roll a fair die 5 times.
• NE = number of evens,
• NT = number of threes or fives
• N1 = number of 1s

Count Arrangements

Empirical (Data) vs. Model (World)

Empirical (Data)

• DATA: x1, x2, …, xn (lowercase)

• The sample that we have to work with
• Summary statistic that minimizes the empirical risk

Model (World)

• Random Variables: X1, X2, …, Xn (uppercase) • Probability distribution from, e.g., a SRS from the population

• Probability parameter that minimizes the Risk

Question

What is the typical wait time for a PG&E (Pacific Gas and Electricity) repair?

Context: PG&E must report to a utilities commission about its service record.