Set α >1. Tahe Xt> , and define a rove b)rove thet Xe X4Xa c)Trove that...
Set α >1. Tahe Xt> , and define a rove b)rove thet Xe X4Xa c)Trove that lim Xn- Set α >1. Tahe Xt> , and define a rove b)rove thet Xe X4Xa c)Trove that lim Xn-
Let B C R" be any set. Define C = {x € R" | d(x,y) < 1 for some y E B) Show that C is open.
19. A cone in R^ is a set C such that if xe C, then Àxe C for all scalars 1>0. A finite cone satisfies the definition (3). Define a cone in R’ that isn't a finite cone.
We define the set X ⊆ L^∞ by X = { {xn} ∈ L^∞ : lim n→∞ xn = 1 } Prove that the set X with the subspace metric d∞|X×X is a complete metric space.
4. Define the seque 1 1 Xn = 1 .+ 22 + 32 +...+ 12 for n > 1. Show that (Xn) is convergent by showing that it is Cauchy. Hint: Use the inequality 1 1 (m + 1)2 = m(m +1) 1 m 1 m +1°
III. (15 pts total) a) Define what it means for a set SCR to be compact. b) Consider the set S = {CERO <<<1}. Give an example of an open cover of S that has a finite subcover. c) With S as above, show that S is not compact by giving an ex- ample of an open cover that does not admit a finite subcover. Justify your answer.
Im wondering how to do b). (6) We define the set of compactly supported sequences by qo = {(zn} : there exists some N > 0 so that Zn = 0 for all n >N). We define the set of compactly supported rational sequences by A={(za) E ao : zn E Q for all n E N). (a) Prove that A is countable (b) Prove that for 1 S p<oo the set A is dense in P. You may use...
Find the critical values using the information in the table. set Hypothesis α df U – Mo < 0 0.01 Mo < 0 0.25 VA Mo > 0 0.025 u – Mo > 0 0.10 a) critical value: b) critical value: c) critical value: d) critical value:
Suppose X ~ Beta(a, β) with the constants α,β > 0, Define Y- 1- X. Find the pdf of Y.
3. Suppose X ~ Beta(a, β) with the constants α, β > 0, Define Y- 1-X. Find the pdf of Y