好悶 有無人問數

geometric 問唔問得

oblique cone parametric equation 係點搵？

呢題我又未遇過，你有咩條件比左？
最直接係寫左一般cone條式，再將條式用rotation matrix將d variable rotate

http://mathworld.wolfram.com/Cone.html

呢到有standard(right) cone parametric equation，咁個尖尖就同個底個圓既圓心同軸，而家我想搵個尖尖座標唔同CONE 底個圓心同軸既parametric equation

另外搵到既話，我仲想問cone 個開口有無得控制(依家係由height ⊂ (0,h) 都係2π，我想知有無得[0,2π]咁變

x = aucosv
y = ausinv
z = u,
唔係好明你想控制開口既乜野，理論上，開口大細已經可以由呢三條eqt求出（你條link入面有）透過調整a,u，可以決定高低大細
如果你想中心軸偏離，你其實係想rotate個cone，咁就要multiply一個rotation matrix，即係點?
設(x，y，z)係你rotate前既cone上一點，
設X，Y，Z係你rotate x,y,z後既點，
咁(X,Y,Z)=rotation matrix * (x,y,z)，再將plug返原式。
我舉個例，原本cone向上，我將佢沿x-z plane扭t度
咁對於cone上任意一點，X=xcost-zsint （點計出黎有D煩，想知再問）
你個rotation matrix 第一row就會係[cost 0 -sint]，如此類推
再將個關係eliminate左x,y,z就做到

個開口意思係咁，個圓柱個横切面會慢慢由一個圓變成一個點，咁其實即係一個oblique cone 樣啦，我要用電腦畫呢個圖，唔識點樣整

1) 乜野係random variable?

2) Proof T= Z / (U/k)^(1/2)
Z~N(0,1) & U~chi squared dist. with k degrees of freedom, where T is t distribution

1) 乜野係random variable?

2) Proof T= Z / (U/k)^(1/2)
Z~N(0,1) & U~chi squared dist. with k degrees of freedom, where T is t distribution

1) measurable function

可唔可以具體D講 唔用definition咁解釋

可以就咁當佢係一個random number
簡單嚟講，sample space就係個experiment所有random嘅可能性，而random variable就係喺嗰個可能性下所得出嘅一個數字

唔可以當random variable係一個數字
反而上面巴打話 measurable function其實concept上正確 但function唔同number所以一定唔可以咁諗

利申唔完全明白 想要深入d既解釋

f is a measurable function簡單黎講就係preimage of (a, infinity) under f 係一個可以給予"體積"的function

都係唔明, 如果 f(x) 可以寫成 x^2+1
咁random variable 可以寫成乜?
input 係唔係parameter? 同埋 output係唔係叫做 data?

3以上的自然數n可以滿足X的n平方加上Y的n平方等於Z的n平方的自然數XYZ不存在
請試著證明之

請求樓主解答

Stochastic process 有冇研究

Stochastic process 有有研究

1) 乜野係random variable?

2) Proof T= Z / (U/k)^(1/2)
Z~N(0,1) & U~chi squared dist. with k degrees of freedom, where T is t distribution

Measurable function from sample space to R(or any measurable space S)
一般黎講，random variable係一個function將實驗結果轉化為另一個數字（或轉化為另一結果）
但呢個function既domain, target domain同埋function本身都要滿足某D條件，令我地measure probability既時候唔會出問題
而條件就係所謂Measurable function，即係pre-image of any measurable set is measurable

一般人可能難以理解，呢個世界上有一D event係無辦法測量(not measurable)。
我係[0,1]均勻分佈抽一個數字，果個數字係[1/2,1]入面既機率自然係1/2。但某D SET我係會講唔出，抽中係入面既機率係幾多。並唔係所有subset of [0,1]可以被測量機率


至於2，其實都係搵返佢個pdf就QED，但個PROOF太長，我SKETCH
將
T= Z / (U/k)^(1/2)
V= U
睇成係一個(Z,U)->(T,V)既transformation，用Jacobian 搵個jpdf
最後int 返T個marginal pdf，就會係t-distribution既pdf

1) 乜野係random variable?

2) Proof T= Z / (U/k)^(1/2)
Z~N(0,1) & U~chi squared dist. with k degrees of freedom, where T is t distribution

Measurable function from sample space to R(or any measurable space S)
一般黎講，random variable係一個function將實驗結果轉化為另一個數字（或轉化為另一結果）
但呢個function既domain, target domain同埋function本身都要滿足某D條件，令我地measure probability既時候唔會出問題
而條件就係所謂Measurable function，即係pre-image of any measurable set is measurable

一般人可能難以理解，呢個世界上有一D event係無辦法測量(not measurable)。
我係[0,1]均勻分佈抽一個數字，果個數字係[1/2,1]入面既機率自然係1/2。但某D SET我係會講唔出，抽中係入面既機率係幾多。並唔係所有subset of [0,1]可以被測量機率


至於2，其實都係搵返佢個pdf就QED，但個PROOF太長，我SKETCH
將
T= Z / (U/k)^(1/2)
V= U
睇成係一個(Z,U)->(T,V)既transformation，用Jacobian 搵個jpdf
最後int 返T個marginal pdf，就會係t-distribution既pdf

1) 乜野係random variable?

2) Proof T= Z / (U/k)^(1/2)
Z~N(0,1) & U~chi squared dist. with k degrees of freedom, where T is t distribution

Measurable function from sample space to R(or any measurable space S)
一般黎講，random variable係一個function將實驗結果轉化為另一個數字（或轉化為另一結果）
但呢個function既domain, target domain同埋function本身都要滿足某D條件，令我地measure probability既時候唔會出問題
而條件就係所謂Measurable function，即係pre-image of any measurable set is measurable

一般人可能難以理解，呢個世界上有一D event係無辦法測量(not measurable)。
我係[0,1]均勻分佈抽一個數字，果個數字係[1/2,1]入面既機率自然係1/2。但某D SET我係會講唔出，抽中係入面既機率係幾多。並唔係所有subset of [0,1]可以被測量機率


至於2，其實都係搵返佢個pdf就QED，但個PROOF太長，我SKETCH
將
T= Z / (U/k)^(1/2)
V= U
睇成係一個(Z,U)->(T,V)既transformation，用Jacobian 搵個jpdf
最後int 返T個marginal pdf，就會係t-distribution既pdf

好, 證實你勁過我個lecturer, 佢話T= Z / (U/k)^(1/2) 冇proof 而係by definition
我冇記錯最後好似係converge in distribution to T?

1) 乜野係random variable?

2) Proof T= Z / (U/k)^(1/2)
Z~N(0,1) & U~chi squared dist. with k degrees of freedom, where T is t distribution

Measurable function from sample space to R(or any measurable space S)
一般黎講，random variable係一個function將實驗結果轉化為另一個數字（或轉化為另一結果）
但呢個function既domain, target domain同埋function本身都要滿足某D條件，令我地measure probability既時候唔會出問題
而條件就係所謂Measurable function，即係pre-image of any measurable set is measurable

一般人可能難以理解，呢個世界上有一D event係無辦法測量(not measurable)。
我係[0,1]均勻分佈抽一個數字，果個數字係[1/2,1]入面既機率自然係1/2。但某D SET我係會講唔出，抽中係入面既機率係幾多。並唔係所有subset of [0,1]可以被測量機率


至於2，其實都係搵返佢個pdf就QED，但個PROOF太長，我SKETCH
將
T= Z / (U/k)^(1/2)
V= U
睇成係一個(Z,U)->(T,V)既transformation，用Jacobian 搵個jpdf
最後int 返T個marginal pdf，就會係t-distribution既pdf

1) 果個 我可唔可以理解成
Random Variable is to quantify an event into a measurable function.
姐係將一D EVENT function化 , 咁呢個function就叫R.V.

1) 乜野係random variable?

2) Proof T= Z / (U/k)^(1/2)
Z~N(0,1) & U~chi squared dist. with k degrees of freedom, where T is t distribution

Measurable function from sample space to R(or any measurable space S)
一般黎講，random variable係一個function將實驗結果轉化為另一個數字（或轉化為另一結果）
但呢個function既domain, target domain同埋function本身都要滿足某D條件，令我地measure probability既時候唔會出問題
而條件就係所謂Measurable function，即係pre-image of any measurable set is measurable

一般人可能難以理解，呢個世界上有一D event係無辦法測量(not measurable)。
我係[0,1]均勻分佈抽一個數字，果個數字係[1/2,1]入面既機率自然係1/2。但某D SET我係會講唔出，抽中係入面既機率係幾多。並唔係所有subset of [0,1]可以被測量機率


至於2，其實都係搵返佢個pdf就QED，但個PROOF太長，我SKETCH
將
T= Z / (U/k)^(1/2)
V= U
睇成係一個(Z,U)->(T,V)既transformation，用Jacobian 搵個jpdf
最後int 返T個marginal pdf，就會係t-distribution既pdf

1) 果個 我可唔可以理解成
Random Variable is to quantify an event into a measurable function.
姐係將一D EVENT function化 , 咁呢個function就叫R.V.

咁又唔係，EVENT還EVENT，RV還RV
X係RV，{X=1}先係EVENT
一般你當R.V.係outcome或function of outcome就OK

可唔可以教多少少double同triple integral點樣定個parametric representations?
認真唔撚識轉 唔撚明點做change of variables

2c我做到greens轉polar coordinate之後做唔到

int(Pdx+Qdy)=int int (Q_x-P_y) dxdy
但Q_x-P_y係1喎 答案咪個DISK既AREA

weak topology of normed vector space係咪metrizable?

唔知
我仲weak過weak topology

weak topology of normed vector space係咪metrizable?

唔知
我仲weak過weak topology

The weak topology is not metrizable as long as the space is infinite dimensional.

weak topology of normed vector space係咪metrizable?

唔知
我仲weak過weak topology

The weak topology is not metrizable as long as the space is infinite dimensional.

算子代數巴打

weak topology of normed vector space係咪metrizable?

唔知
我仲weak過weak topology

The weak topology is not metrizable as long as the space is infinite dimensional.

算子代數巴打

算子代數好難