STA104/MTH135: Probability

Homework #3: Binomial & Normal

Due: Thursday, Sep 18

Text Problems are from Jim Pitman, Probability (1st edn).

• Exercises
  

  § 2.1:		1	5	10	13
  § 2.2:		1	3	9	13
  § 2.3:		1	2

• Another Problem (Optional, XC)
  We suspect that our die might be biased- and so the probaility of an ace might not be exactly 1/6. Let's count the number X of times an Ace appears in N independent rolls, and estimate the probabliity p of an ace as the frequency X/N of aces in the first N rolls (an "Ace" is just a roll of 1).
  
  How big must N be to ensure that the probability P[ |p - X/N| < 0.01] is at least 0.99--- i.e., how large a sample do we need to ensure that the estimate X/N of the probability p of an ace for a possibly-unfair die will be within ±0.01 of the correct answer, with probability at leaast 0.99 ?
  
  In class I showed that N=16587 was big enough, by using a normal approximation and being careless about the ±½ terms. See if you can do better--- either by being careful about the ±½ terms, or using Matlab or R to compute the binomial distribution probabilities without using a normal approximation. Show your work. Would it help if you assume 0.10 < p < 0.20???

Good Luck!