Recent content by Obraz35

Homework Statement \[P^{'}(t)+(\lambda +\mu )P(t)=\lambda \] I have never worked with differential equations before and I am trying to work off of the one example we did in class, but I can't figure out where I am going wrong. Homework Equations The Attempt at a Solution...

Homework Statement Let X be the number of 1's and Y be the number of 2's that occur in n rolls of a fair die. Find Cov(X, Y) Homework Equations Cov(X,Y) = E(XY) - E(X)E(Y) The Attempt at a Solution Both X and Y are binomial with parameters n and 1/6. Thus it is easy to find E(X)...

Homework Statement The probability mass function of a random variable X is: P(X=k) = (r+k-1 C r-1)pr(1-p)k Give an interpretation of X. Homework Equations The Attempt at a Solution The PMF looks like the setup for a binomial random variable. The first combination looks like you...

Homework Statement Show that if A1, A2, ..., An are independent events then P(A1 U A2 U ... An) = 1 - [1-P(A1)][1-P(A2)]...[1-P(An)] Homework Equations If A and B are independent then the probability of their intersection is P(A)P(B). The same can also be said of AC and B. The...

Homework Statement Let G be a finite group. Prove that if some conjugacy class has exactly two elements then G can't be simple Homework Equations The Attempt at a Solution I originally proved this accidentally assuming that G is abelian, which it isn't. So say x and y are...

Here is my idea although it may be way off the mark. Still looking at p=3, the subgroup could contain powers of 10 different 9-cycles that way you'd have 80 different elements plus the identity. I think that works. Although I guess we can't be sure that it's closed. Well, I'm basically out of...

Okay, that's true. Sorry. I guess I really just have no idea how to find generators for this. I was trying with p=3 for my example and found that 3^4 is the highest power of 3 that divides 9! since there are 4 factors of 3 in 9*8*7*6*5*4*3*2*1. So the Sylow p-subgroup would have 81 elements. So...

Sorry, it's supposed to be restricted to just odd primes, in which case I think that still holds, correct?

Homework Statement Find a set of generators for a p-Sylow subgroup K of Sp2 . Find the order of K and determine whether it is normal in Sp2 and if it is abelian. Homework Equations The Attempt at a Solution So far I have that the order of Sp2 is p2!. So p2 is the highest power of...

Homework Statement Let G be a finite abelian group and let #(n) signify the number of elements x in G which satisfy x^n = e. Find the torsion coefficients of G when #(2)=16, #(4)=32, #(3)=9, #(9)=81 and x^36=e for all x in G. Homework Equations The Attempt at a Solution I really...

Homework Statement If J is a subgroup of G whose order is a power of a pirme p, prove that J must be contained in a Sylow p-subgroup of G. (Take H to be a Sylow p-subgroup of G and let X be the set of left cosets of H. Define an action of G on X by g(xH) = gxH and consider the induced action...

Well, my guess is that the number of rotational symmetries for the new object is less than the number for the original dodecahedron. I would guess it's dihedral or icosahedral (since I know of one axis with order 5) symmetry even though I do see a couple of problems with those theories, but I...

Maybe this doesn't make sense, but I don't see how the edges of the square can be in the same orbit as the edges that only border hexagons.

Homework Statement Let G be the group of rotational symmetries of the octahedron and consider the action of G on the edges of the truncated octahedron. Describe the orbits of this action. Choose one representative element in each orbit. Describe the stabilizers of these representative...

Would the last two 3-cycles really be fixed? If there were six elements remaining to put into cycles there are still 20 different ways to put them into two separate 3-cycles, correct?