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!
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...
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?
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...
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...
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
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...
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...
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...
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?
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?
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...
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!
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...
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?
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?
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...
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...