Stat 110 Strategic Practice 2, Fall 2011
Prof. Joe Blitzstein (Department of Statistics, Harvard University)
1
Inclusion-Exclusion
1. For a group of 7 people, nd the probability that all 4 seasons (winter, spring,
summer, fall) occur at least once each am
Stat 110 Strategic Practice 1, Fall 2011
Prof. Joe Blitzstein (Department of Statistics, Harvard University)
1
Naive Denition of Probability
1. For each part, decide whether the blank should be lled in with =, <, or >, and
give a short but clear explanati
Stat 110 Strategic Practice 5, Fall 2011
Prof. Joe Blitzstein (Department of Statistics, Harvard University)
1
Poisson Distribution and Poisson Paradigm
1. Raindrops are falling at an average rate of 20 drops per square inch per minute.
What would be a re
Stat 110 Strategic Practice 3, Fall 2011
Prof. Joe Blitzstein (Department of Statistics, Harvard University)
1
Continuing with Conditioning
1. Consider the Monty Hall problem, except that Monty enjoys opening Door 2
more than he enjoys opening Door 3, and
Stat 110 Strategic Practice 6, Fall 2011
Prof. Joe Blitzstein (Department of Statistics, Harvard University)
1
Exponential Distribution and Memorylessness
1. Fred (the protagonist of HW 6 #1) wants to sell his car, after moving back
to Blissville (where h
Stat 110 Strategic Practice 7, Fall 2011
Prof. Joe Blitzstein (Department of Statistics, Harvard University)
1
Joint, Conditional, and Marginal Distributions
1. A random point (X, Y, Z) is chosen uniformly in the ball B = cfw_(x, y, z) :
x2 + y 2 + z 2 1.
Stat 110 Strategic Practice 10, Fall 2011
Prof. Joe Blitzstein (Department of Statistics, Harvard University)
1
Conditional Expectation & Conditional Variance
1. Show that E(Y
E(Y |X)2 |X) = E(Y 2 |X)
pressions for Var(Y |X) agree.
(E(Y |X)2 , so these tw
Stat 110 Strategic Practice 8, Fall 2011
Prof. Joe Blitzstein (Department of Statistics, Harvard University)
1
Covariance and Correlation
1. Two fair six-sided dice are rolled (one green and one orange), with outcomes
X and Y respectively for the green an