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  1. F

    If variance is 0, then p(x=c) = 1 c is constant

    I think it is easy but I can't figure it out. :( any help?
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    Recursive question

    Suppoese T(0) = 1 T(n) = T(n-1) + root(T(n-1)) how many recursion does T(n) need to grow to the number k? can I get this? root(k) < m < c root(k) c is constant and m is the times we need for T(n) goes to k. Any help appreciated!!
  3. F

    Recursive question

    Suppoese T(0) = 1 T(n) = T(n-1) + root(T(n-1)) how many recursion does T(n) need to grow to the number k? can I get this? root(k) < m < c root(k) c is constant and m is the times we need for T(n) goes to k. Any help appreciated!!
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    Probability questions?

    Thanks a lot. Yes I made a mistake here, the latter should be j -> m-1. Your advice is really helpful..
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    Probability questions?

    Yes, the buckets are labeled from 0 to m-1, the probaiblity that a ball going to buckets(from 0 to j-1) is 0.9, and going to j-1 to m-1 bucket is 0.1. and inside [0, j-1] and [j-1, m-1] is equally. j is only a number. for example if m=4, j=2 and p(a ball go to bucket 0,1) = 0.9 and p(go to...
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    Probability questions?

    How to calculate the probability of this questions? Supposed there are m bukcets, n balls. use function f(x) to decide which bucket the ball go. Supposed that the probability a ball going to 0-j is 0.9 and going to j -> m-1 is 0.1. What's the probability of for every bucket there is at...
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    NFA Problem

    sorry. sorry about that, man. But if you google 'NFSA assignment', you will find that some people name it NFSA, most call it NFA. Since My professor call it NFSA, there is nothing I can do about it and I had to follow him.
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    NFA Problem

    Thanks U r smart! man.. however, it seems that it only accepts the string end with 1 ocurred even times, not 0. and '01' is also accepted by it. it is not we wanted. Actually, After spending serveral nights on it. I also figure out a way using six states to accept a string end both 1 and 0...
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    NFA Problem

    it should be 'non-deterministic FSA ' non-deterministic FSA
  10. F

    NFA Problem

    Is that possible using six states to draw a NFSA(NFA) to represent a string ending with a symbol which occured even times in this string(this string is consisted of only 0 and 1).. I thought that the regular expression is (0*10*1)*(0*10*1) + (1*01*0)*(1*01*0), It can be easy using 7 states to...
  11. F

    Does x->infiity (ln |cosx|)/x^2 exist?

    still not get it.. How can I explain that: ln|cosx| grows faster than x^2 if x>X for some X?
  12. F

    Does x->infiity (ln |cosx|)/x^2 exist?

    Does x->infiity (ln |cosx|)/x^2 exist?? I can't apply apply L'Hopital here, since the limit of |cosx| doesn't exist.. Any hints appreciated..
  13. F

    Non-recursive formula

    I have already wrote down previous 20 items, still can't find the relationship I have already wrote down previous 20 items, still can't find the relationship
  14. F

    Non-recursive formula

    How to get a non-recursive formula for y(n): y(n)=1 (n=1 or 2) y(n)=0 (n=3 or 4) y(n)=(y(n-4) + y(n-3))/2 Any hints apprecaited..
  15. F

    How to work that out?

    Thank you so much! U r so helpful, man. thanx!
  16. F

    Connectives homework

    Thanks! Anyway, thanks a lot to all guys!
  17. F

    Connectives homework

    {<->, ~} is not a complete set of connectives.. It seems that we can't use Propostions P is all true and thus lead to contradition since ~ can make it false. Any suggestion?
  18. F

    How to work that out?

    sorry, man, I made a mistake here, the second one should be: ((A & C) v (~C & B)), it should be equivalent.
  19. F

    How to work that out?

    1) (C -> A) and (!C -> B) 2) (A and C) or (!C and B) I use the logic calculator and found these two formulas are logical equivalent, but I spend 2 hours there and still can't prove it because I can't eliminate one of the three items. Can anyone help me? Thanks in advance!
  20. F

    Prove the algorithm for LCM

    U right.. I forget to mention that.. m,n>=1 is the precondition..
  21. F

    Prove the algorithm for LCM

    loop invariant.. the loop invariant should be 1)ak >=m and bk> =m 2)ak mod m=0 and bk mod n=0 3)ak<=lcm(m,n) and bk<=lcm(m,n) U can prove a is the lcm(m,n) by these LI..
  22. F

    Help me about loop invariant of LCM

    Forget it! problem soloved ... Forget it! problem soloved ... :smile:
  23. F

    Prove the algorithm for LCM

    Forget it! problem soloved ... Forget it! problem soloved ...
  24. F

    Prove the algorithm for LCM

    algorithm to prove lcm: a:=m b:=n while a != b if a < b a:= a + m else b:= b + n //postcondition: a is the lcm(m,n) what's the loop invariant?I thought it is(not sure): lcm(ak, bk) = lcm(ak/m, bk/n) *lcm(m,n) I am not sure and also impossible to prove my loop invariant...
  25. F

    Help me about loop invariant of LCM

    please help me, i was stuck in here 2 days!!! algorithm to prove lcm: a:=m b:=n while a != b if a < b a:= a + m else b:= b + n //postcondition: a is the lcm(m,n) what's the loop invariant?I thought it is(not sure): lcm(ak, bk) = lcm(ak/m, bk/n) *lcm(m,n) I am...
  26. F

    Integration Problem.

    Thanks so much. I got it!
  27. F

    Integration Problem.

    integrate ln(tanx)/sinxcosx dx I want to change to integrate csc2x ln(tanx) dx , still can't work it out. Any suggestions? THX
  28. F

    Non-trivial equation

    Another question root(3)=(m+3n)/(m+n), if m,n is allowed having the common factor,Does it lead to any contradiction?
  29. F

    Non-trivial equation

    thanx a lot! thanks a lot to all you guys! really appreciated..
  30. F

    Non-trivial equation

    1)write root(3)-1 in another way,and use this to produce a non-trivial equation for root(3) in terms of itself 2)suppose m,n(m,n is natural numbers) are such that m/n=root(3),use (1) to write root(3)as another combination of m and n. 3)use (2) to show that root(3) in not rational. Any...
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