Recent content by scottstapp

Homework Statement Suppose we want to estimate a binomial proportion, p. We take a sample of size n and count X successes. Consider a Bernoulli random variable, Y that is 1 with probability p and 0 otherwise. Show that the mean and variance of Y are p and p(1-p), respectively...

No, I do not want to prove F(n+1)-F(n)=1/((n+1)*(n+2)). Here is my algebra for my last step, maybe it will clarify things: once we let n=t-1 and plug it into (n/(n+1))+(1/t)(1/t+1) we get the following: ((t-1)/t)+(1/(t(t+1))) finding a common denominator gives ((t+1)(t-1)+1)/(t(t+1))...

Thank you statdad I believe this helped but am still curious about my step (2). Here is what I have changed: (1)Let S be the set of all positive integers k such that 1/2+(1/2)(1/3)+...+(1/k)(k+1)= n/(n+1) (2) 1 is in S because (1/1)(1/2)=1/2 which is in S (not sure if this is the correct...

Homework Statement This is my first proof by induction so I need some assistance If n is a positive integer, then \sum1/(k(k+1))from k=1 to n is equal to n/(n+1) Homework Equations I'm not sure if this is useful for this proof but we are given the proposition: let n be a positive...

Homework Statement Reduce 34567 modulo 19. Homework Equations The Attempt at a Solution I approached by first reducing 4567 modulo 18. I got the following: 34567= 318*253+13=(318)253*313 congruent to 12531594323 congruent to 14 mod 19 Is this the correct approach? I am not...

I guess what I was trying to ask was is the way I wrote a valid formal proof?

Homework Statement Prove the following a is congruent to s(mod 9) Homework Equations a=drdr-1***d1d0 a=d0+ d110+ d2102+...+dr10r s= d0+ d1 +...+dr The Attempt at a Solution we know that 10-1=9 so we can say that 10 is congruent to 1(mod 9) so we know that a is congruent to d0+ d110+...

Homework Statement I need to prove the following but have no idea how to do so. Let a,b, k be integers with k positive. If a is congruent to b(mod n), then ak is congruent to bk (mod n). Homework Equations The hint given is that I can assume the following proposition is true and that...

In this problem can I actually just multiply through by -1 though? I am supposed to have a positive x and a positive y. So doesn't that mean that there does not exist any positive x and y such that 1234x-4321y=1? I know this seems to be a very elementary question but by the terms of this...

Can you explain to me how you got 1182? Is my entire bottom row incorrect?

Homework Statement Find a positive integer solution to 1234x-4321y=1, both x and y will be positive. Homework Equations The Attempt at a Solution I created this array 4321 1234 619 615 4 3 1 3 1 1 153 1 1082 309 155 154 1 1...

Thanks owlpride, that's what I was thinking but I just needed some reassurance.

Homework Statement I just have a general question. Suppose a,b and c are integers with a and b not both 0. There exists d=gcd(a,b) and ax+by=c. From this I know that d|a and d|b but how do I know that there exists x,y such that d|(ax+by) where ax+by does not equal d and d|c ? I cannot...

I was just looking at Euclids Lemma actually and wondering how I would prove that c|ab? Is it because c is relatively prime with each a therefore it must divide ab? Thank you for your help once again

Homework Statement I have to prove the following: Let a1,a2, ...,an be integers and set b=a1*a2*...*an. If c is a nonzero integer and c is relatively prime to each ak, then c and b are relatively prime.Homework Equations Definition of relatively prime: Let a and b be integers, not both zero...