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cs-312:hw8 [2014/12/31 22:58]
ringger created
cs-312:hw8 [2014/12/31 23:22] (current)
ringger
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-__NOTOC__ +Homework Assignment #8 =
-<​big>'''​Homework Assignment #8'''</​big>​+
  
 == Objective == == Objective ==
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 Let's define a simple experiment as follows: ​ Roll two dice.  Each sample (outcome) is an ordered pair of die faces. Let's define a simple experiment as follows: ​ Roll two dice.  Each sample (outcome) is an ordered pair of die faces.
 * How many samples are in the sample space? * How many samples are in the sample space?
-Now define a random variable ​<​math>​X</​math>​which assigns to each sample the total number of dots on the faces of the two dice.  Also, assume a uniform distribution over samples. +Now define a random variable ​$X$which assigns to each sample the total number of dots on the faces of the two dice.  Also, assume a uniform distribution over samples. 
-* What is the probability ​<​math>​p(X=7)</​math> ​with these fair dice?+* What is the probability ​$p(X=7)with these fair dice?
 * What is the probability of rolling the outcome "snake eyes" (two ones) with these fair dice? * What is the probability of rolling the outcome "snake eyes" (two ones) with these fair dice?
-* What is the expected value of our random variable ​<​math>​X</​math> ​with respect to this fair distribution?​+* What is the expected value of our random variable ​$Xwith respect to this fair distribution?​
  
 ===Question 2=== ===Question 2===
 Probability Theory: Probability Theory:
  
-Let's define another simple experiment involving rolling two dice as follows: again, each sample (outcome) is an ordered pair of die faces, and we define a random variable ​<​math>​X</​math>​which assigns to each sample the total number of dots on the faces of the two dice.  This time assume that the dice are "​loaded"​ (in other words, not fair) and that for each die the probability of rolling a 1 is 1/4, while the other outcomes for each die share the remaining 3/4 probability mass equally. +Let's define another simple experiment involving rolling two dice as follows: again, each sample (outcome) is an ordered pair of die faces, and we define a random variable ​$X$which assigns to each sample the total number of dots on the faces of the two dice.  This time assume that the dice are "​loaded"​ (in other words, not fair) and that for each die the probability of rolling a 1 is 1/4, while the other outcomes for each die share the remaining 3/4 probability mass equally. 
-* What is the probability ​<​math>​p(X=7)</​math> ​with these loaded dice?+* What is the probability ​$p(X=7)with these loaded dice?
 * What is the probability of rolling the outcome "snake eyes" (two ones) with these loaded dice? * What is the probability of rolling the outcome "snake eyes" (two ones) with these loaded dice?
-* What is the expected value of our random variable ​<​math>​X</​math> ​with respect to this unfair distribution?​+* What is the expected value of our random variable ​$Xwith respect to this unfair distribution?​
  
 ===Question 3=== ===Question 3===
 Recurrence Relations: Recurrence Relations:
  
-Suppose an algorithm has running time described by the following recurrence relation: ​<​math>​T(n) = 3 T(n/4) + n^2</​math>​.  Use the theory of recurrence relations to solve this recurrence relation. ​ Come up with the general solution and then place it in an asymptotic order of growth.+Suppose an algorithm has running time described by the following recurrence relation: ​$T(n) = 3 T(n/4) + n^2$.  Use the theory of recurrence relations to solve this recurrence relation. ​ Come up with the general solution and then place it in an asymptotic order of growth.
  
cs-312/hw8.txt · Last modified: 2014/12/31 23:22 by ringger
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