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lect04, Thu 04/09
HW 1 due tomorrow
HW 2 out tomorrow (due in 2 weeks)
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
Empirical (Data) vs. Model (World)
DATA: x1, x2, …, xn (lowercase)
- The sample that we have to work with
- Summary statistic that minimizes the empirical risk
• Random Variables: X1, X2, …, Xn (uppercase) • Probability distribution from, e.g., a SRS from the population
- Probability parameter that minimizes the Risk
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.