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

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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(AB) ?
What is the P(AB) ?
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(AB) ?
What is the P(AB) ?
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]?
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