# Search results

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...

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 :)