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1. 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.
2. 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!
3. 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...
4. 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?
5. 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...
6. 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...
7. 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?!?
8. Normally distributed probability problem

oh and n = total so in this case 12
9. 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 :)
10. 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
11. 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...
12. 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...
13. Proving lim (as n -> infinity) 2^n/n! = 0

i see where you're going but where does that final 2/3 come from?
14. 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...
15. Correlation and independence in Probability

ah okay - thank you! i had misread what had been previously typed about that, i do apologise
16. Correlation and independence in Probability

but that is what i indeed went away and did and this gave me that E(XY) = E(X)E(Y) which implies independence. That is the only way i know how to/have been taught how to work out whether two random variables are independent or not. Therefore is there another way?
17. Correlation and independence in Probability

exactly and that's why i'm really confused...i think this must be a special case or something.
18. Correlation and independence in Probability

Okay so I'll work with pmf's instead, but then for example finding P{X=0 and Y=0} = P{X=0 and X2=0} = P{X=0}P{X2=0|X=0} would that be equal to 1/3 * 1 as P{X2=0|X=0} that is one?
19. Correlation and independence in Probability

1. Homework Statement Let X be a random vairable which can only take three values: -1,0,1 and they each have the same probability. Let Y also be a random vairable defined by Y = X2. Show that i) X and Y are not independent ii) X and Y are uncorrelated 2. Homework Equations To show...
20. First order differentials

Okay so does that mean that what jeffreydk would not work? If so what can i use instead? I have only been taught about linear first order d.e so really don't know what to do!
21. First order differentials

1. Homework Statement Solve: (2t+x) dx/dt + t = 0 2. Homework Equations y' +p(X)y = q(x) and y(x) = (\intu(x)q(x) + c)/u(x) where u(x) = e\intp(x)dx Note this u(x) is 2 to the power of the integral of p(x) 3. The Attempt at a Solution (2t+x) dx/dt + t = 0 becomes: dx/dt + t/(2t+x) = 0 by...
22. Proof by induction

But i don't understand how you rearranged an equation to get n2 - 2n- 1 and then once i've found which values of n this equation holds true for, how does this show 2 n+1 > 4(n+1)2 + 1?
23. Proof by induction

Okay so disregarding my previous questions for the time being, In answer to your question about for which n values does it hold true, I did it like this: n2- 2n- 1> 0. (n-1)2 - 2 > 0 (n-1)2 > 2 (n-1) > 4 n > 5 So for values greater than 5?
24. Proof by induction

But still.... are you just rearranging this because if so how does it change to >> and why is it -4 and not -3?
25. Proof by induction

Hang on, no I think i see what you were doing now....I'll just have a go :)
26. Proof by induction

Is that last bit right? Because I multiplied it out to be 8n2 + 16n + 10?
27. Proof by induction

1. Homework Statement Prove that (\foralln in the set of Natural numbers )[(n \geq 9) \Rightarrow (2n > 4n2 + 1)] 2. Homework Equations To do proof by induction you must first prove for n = 1, then assume true for n and then show for n+1 3. The Attempt at a Solution So for n=1 i have...
28. Marginal/Conditional Probability Mass Functions

1. Homework Statement A bag contains four dice labelled 1,...,4. The die labelled j has j white faces and (6-j) black faces, j = 1,...,4. A die is chosen at random from the bag and rolled. We define X = the number labelling the chosen die. Y = {0 if the face showing on the die is black; 1 if...
29. Finding x = ymod(n) for x=2^71 and n=23

because I'm appalling at Number Theory so normally I'm wrong :-P
30. Analysis: proving inverses involving sets

oh okay, thank you very much :)