Search results

  1. ichabodgrant

    Probability question on fair coin

    thank you for your kindness
  2. ichabodgrant

    Probability question on fair coin

    so the probability of getting HH is p2? Then the required probability is 1- p2?
  3. ichabodgrant

    Probability question on fair coin

    If it is HT, then no matter the next one is T or H, TH already occurs before HH, right? If it is TT, then also no matter the next one is T or H, TH already occurs before HH, right? If it is TH, then obviously no matter the next one is T or H, TH already occurs before HH, right? Just the case if...
  4. ichabodgrant

    Probability question on fair coin

    so if there is no HH, then it is alright? Let the probability of getting a H be p. Then the required prob. is 1 - p2?
  5. ichabodgrant

    Probability question on fair coin

    Actually TT, HT,TH all means TH must occur before HH, right?
  6. ichabodgrant

    Probability question on fair coin

    Should I indeed use conditional probability? In case I have a T at the 1st trial, then it already achieves the event that TH appears before HH?
  7. ichabodgrant

    Probability question on fair coin

    Oh Sorry... I have a typo in the question... The correct question is "T,H before HH"
  8. ichabodgrant

    Probability question on fair coin

    but it seems 0.5*0.5*0.5*... , gets you 0...
  9. ichabodgrant

    Probability question on fair coin

    Which two? TH and HT? 0.5*0.5 + 0.5*0.5 = 0.5?
  10. ichabodgrant

    Probability question on fair coin

    So simply calculate the first case?
  11. ichabodgrant

    Probability question on fair coin

    I don't quite understand your question... The prob. of getting a head or a tail is 1/2? Is this what you are asking?
  12. ichabodgrant

    Probability question on fair coin

    Homework Statement A fair coin is continually flipped. What is the probability that the pattern T,H occurs before the pattern H,H, where T and H respectively denote Tail and Head of a coin? Homework Equations Prob. = (n r) (pr)(1-p)n-r The Attempt at a Solution I am thinking whether the...
  13. ichabodgrant

    Probability and normal distribution

    because question 1 is P(acceptable)...so I use it directly...
  14. ichabodgrant

    Probability and normal distribution

    So is this P(more than 2 tests) = 1 - [ P(1st acceptable) + P(1st rejected, 2nd accpetable) ] = 1 - [ p + (1-p)p ] wrong?
  15. ichabodgrant

    Probability and normal distribution

    I understand 1st and 3rd question now. For 2nd question, my approach now is let p be the P(accpetable) in 1st question. P(more than 2 tests) = 1 - [ P(1st acceptable) + P(1st rejected, 2nd accpetable) ] = 1 - [ p + (1-p)p ]. Is this correct?
  16. ichabodgrant

    Probability and normal distribution

    Homework Statement Due to the pollution from the industry around an apple farm, the apples grown there may be contaminated by heavy metals. It is believed that the amount of heavy metals in an apple of the farm follows the Normal distribution. N(16,16) which has a mean μ = 16 units and σ = √16...
  17. ichabodgrant

    Prove arcsin x for its logarithm form

    Homework Statement Given sin x = (eix - e-ix) / 2i, I want to prove that arcsin x = -i ln(ix + √1 - x2) Homework Equations I know about the Euler's formula and complex number. But I have never learnt about complex logarithms. The Attempt at a Solution I try to use x = sin y. But it seems...
  18. ichabodgrant

    Decomposition using roots of unity

    Sorry. My typo... It should be (e2πi/5)5, so it equals 1.
  19. ichabodgrant

    Decomposition using roots of unity

    I can solve it now. Thanks.
  20. ichabodgrant

    Decomposition using roots of unity

    You mean I can make two pairs into the form (x−r)(x−r∗) that makes them real?
  21. ichabodgrant

    Decomposition using roots of unity

    You mean this pair are conjugates to each other?
  22. ichabodgrant

    Decomposition using roots of unity

    I can get (x - 1)(x4 + x3 + x2 + x + 1), but then what to do? To decompose (x4 + x3 + x2 + x + 1) into 2 more?
  23. ichabodgrant

    Decomposition using roots of unity

    Homework Statement Decompose x5 - 1 into the product of 3 polynomials with real coefficients, using roots of unity. Homework Equations As far as I know, for xn = 1 for all n ∈ ℤ, there exist n distinct roots. The Attempt at a Solution [/B] So, let ω = e2πi/5. I can therefore find all the 5th...
Top