Recent content by pp123123

I have drawn such a graph, but the two different methods of decomposition under a negative price change of commodity X have revealed two different natures of commodity X - the Slutsky decomposition concludes that X is normal, while the Hicksian decomposition yields the opposite conclusion. Is...

I came across some summation but have no idea how to simplify it. $\sum_{x=0}^{\infty} \binom{x+r-2}{r-2}(1-p)^{x}=p^{1-r}$ Why is it so?

Oh I get it. So is it okay to write something like: Due to the fact that $L^{-1}L_1 = UU_1^{-1}$ The resulting matrix must be a diagonal matrix under the circumstances that it must both be a lower-triangular and upper-triangular matrix. Denote $D$ as the desired diagonal matrix. $L^{-1}L_1 =...

Just came across LU decomposition and I am not sure how to work on this problem: Let L and L1 be invertible lower triangular matrices, and let U and U1 be invertible upper triangular matrices. Show that LU=L1U1 if and only if there exists an invertible diagonal matrix D such that L1=LD and...

Homework Statement http://imageshack.com/a/img546/5686/nqpn.jpg I am looking for the probability of the current passing from the left to right given that there are 5 independent switches of probability p. However I cannot figure out the correct solution. Homework Equations The...

Hi guys. Here's the problem. I need to determine the probability that the current could go from left to right given that there is a probability of p for each independent switch named a,b,c,d and e. I have tried to solve this but I have no idea which part I am getting off the right track. Here...