Recent content by vikkisut88

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    Convergence of alternating series

    okay, but i still don't understand how i'm meant to show the result, sorry. This question has got me completely flummoxed.
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    Convergence of alternating series

    sorry i don't really understand that - how did you work out that s was 5/6? And did you just choose random values for a0, a1 and an? I have rechecked my homework question and that is exactly what it said!
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    Convergence of alternating series

    1. Homework Statement Let s be the sum of the alternating series \sum(from n=1 to \infty)(-1)n+1an with n-th partial sum sn. Show that |s - sn| \leqan+1 2. Homework Equations I know about Cauchy sequences, the Ratio test, the Root test 3. The Attempt at a Solution I really have...
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    Finding mean and variance

    Right okay, so now for the variance do I use the same formula but use 1.6 (I presume it was just a typo and it should have been 0.7 *2) instead of 0.53? Do I then use the Central Limit Theorem for part b?
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    Finding mean and variance

    Okay I have since realised that for part a) I think i was doing it wrong so now for the mean I have: ((0.7*2) + (0.2*1) + (0.1*0))/3 = 0.53 But for the Variance I have: ((0.7 - 0.53)2+ (0.2 - 0.53)2 + (0.1 - 0.53)2)/3 = 0.1076 which makes far more sense!! Now I'm thinking of using...
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    Finding mean and variance

    1. Homework Statement Suppose that, on average, 70% of graduating students want 2 guest tickets for a graduation ceremony, 20% want 1 guest ticket and the remaining10% don't want any guest tickets. (a) Let X be the number of tickets required by a randomly chosen student. Find the mean and...
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    Proving that f is bounded on R

    but I can't just assume it is that specific function surely? plus i have to prove it's bounded, not unbounded?!?
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    Normally distributed probability problem

    oh and n = total so in this case 12
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    Normally distributed probability problem

    nope you just have one 12C3 - it's how you use the binomial theorem: P(X=r) = nCr * p^r * q^(n-r) where q = 1-p :)
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    Normally distributed probability problem

    The answer to part a) is correct, however, I don't really understand what calculation you've done for part b). Personally I would just use the Choose function i.e. 12C3 * 0.0301^3 * 0.9699^9
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    Proving that f is bounded on R

    1. Homework Statement Suppose that f: R -> R is continuous on R and that lim (x -> \infty+)(f(x) = 0) and lim (x -> \infty-)(f(x)=0). Prove that f is bounded on R 2. Homework Equations I have got the proof of when f is continuous on [a,b] then f is bounded on[a,b] but I'm unsure as to...
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    Proving that g1,g2,g3 are linearly independent

    1. Homework Statement Let V = {differentiable f:R -> R}, a vector space over R. Take g1,g2,g3 in V where g1(x) = e^{}x, g2(x) = e^{}2x and g3(x) = e^{}3x. Show that g1, g2 and g3 are distinct. 2. Homework Equations If g1-g3 are linearly independent, it means that for any constant, k in F...
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    Proving lim (as n -> infinity) 2^n/n! = 0

    i see where you're going but where does that final 2/3 come from?
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    Proving lim (as n -> infinity) 2^n/n! = 0

    1. Homework Statement Prove that lim n \rightarrow\infty 2^{}n/n! = 0 2. Homework Equations This implies that 2^{}n/n! is a null sequence and so therefore this must hold: (\forall E >0)(\existsN E N^{}+)(\foralln E N^{}+)[(n > N) \Rightarrow (|a_{}n| < E) 3. The Attempt at a...
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    Correlation and independence in Probability

    ah okay - thank you! i had misread what had been previously typed about that, i do apologise
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