Assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) find the critical value
tα/2,
(b) find the critical value
zα/2,
or (c) state that neither the normal distribution nor the t distribution applies.
Here are summary statistics for randomly selected weights of newborn girls:
n=162,
x=30.1
hg,
s=6.1
hg. The confidence level is
99%.
Let AB = Im, where A is an m×n matrix and B is an n×m matrix. If y ∼ MVN(μ,In) and BA is symmetric, find the distribution of yT BAy.
令 AB = Im,其中 A 是 m×n 矩阵,B 是 n×m 矩阵。如果y ∼ MVN( μ ,In) 和 BA 是对称的,求y T BA y的分布。
Definition of polynomial ring
Given a ring R, the polynomial ring is defined as
However, it is not usually specified what x is. In order for multiplication to make sense, I guess it has to be an element in R at least. But is R[x] the set of all functions , or the set of those functions evaluated at x?
Sometimes R is required to be commutative. Does that make any difference for R[x]?