# 10-601 Lecture Notes - Lecture 1: Activity Tracker, Global Positioning System, Binary Tree

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Published on 1 Mar 2019

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Recitation 1

Background

CMU 10-601: Machine Learning (Spring 2019)

Friday, Jan 18th, 2019

1 Probability and Statistics

1. Two events, A and B, are considered disjoint (mutually exclusive). P(A) = 0.5, P(B)

= 0.5.

What is the P(A∪B) ?

What is the P(A∩B) ?

What is the P(A|B) ?

2. Now, instead, the two events A and B are not disjoint, but they are independent.

What is the P(A∪B) ?

What is the P(A∩B) ?

What is the P(A|B) ?

3. A student is looking at her activity tracker (Fitbit/Apple Watch) data and she notices

that she seems to sleep better on days that she exercises. They observe the following:

Exercise Good Sleep Probability

Yes Yes 0.3

Yes No 0.2

No No 0.4

No Yes 0.1

What is the P(GoodSleep =Y es|Exercise =Y es) ?

Why doesn’t P(GoodSleep =Y es ∩Exercise =Y es) = P(GoodSleep =Y es)·

P(Exercise =Y es) ?

The student merges her activity tracker data with her food logs and ﬁnds that

the P(Eatwell =Y es|Exercise =Y es ∩GoodSleep =Y es) is 0.25. What is the

probability of all three happening on the same day?

4. What is the E[X] where X is a single roll of a fair 6-sided dice (S = {1,2,3,4,5,6})? What

is the Var[X]?