機率簡介 | 台灣彩券分店資訊

機率密度函數—(pdf).設X:連續型隨機變數.F(t):X的累積分佈函數.令f(x)=F'(x)或F(x)=,則f(x)稱為X的機率密度函數(pdf)....期望值,變異數,標準離差.

試驗: 連續擲一銅板三次.

= {HHH, HHT, HTH, HTT, TTT, TTH, THT, THH}.

X = 每個 outcome 正面的次數.

P(0) = P(X = 0) = P({TTT}) = 1/8.

P(1) = P(X = 1) = P({HTT, THT, TTH}) = 3/8.

P(2) = P(X = 2) = P({HHT, HTH, THH}) = 3/8.

P(3) = P(X = 3) = P({HHH}) = 1/8.

X的(累積)分佈函數 F(x):

若 x < 0, F(x) = 0. 若 0 x < 1, F(x) = 1/8. 若 1 x < 2, F(x) = 1/2. 若 2 x < 3, F(x) = 7/8. 若 x 3, F(x) = 1.

如: F(-1) = 0, F(0) = 1/8, F(1) = 1/2, F(2) = 7/8, F(3) = F(4) = ... = 1.