2023-10

期待値と分散\(E = E-E = \mu_Y-\mu_X = 0\)\(V = V =V+V -2 S_{XY}\)\( =\sigma^2_Y+\sigma^2_X -2 \rho_{XY}\sigma_X \sigma_Y\)\(=7...

\(f'(x) = 60 (3x^2(1-x)^2 + x^3 \cdot 2(1-x)(-1))\)\( = 60x^2(1-x) (3(1-x) - 2x)\)\( = 60x^2(1-x) (3-5x)=0\)として、\(x=0,\d...

総平方和、回帰平方和、残差平方和をそれぞれ\(S_{yy},S_{R},S_{e}\)とする。決定係数決定係数\(R^2\)は、書籍『統計学』の回帰分析の項にあるように、\(\displaystyle R^2 = 1-\frac{S_{e}...

機械A,Bで発生する不良品の数を表す確率変数を\(X,Y\)とすると、\(X \sim B(m,p)\)\(,Y \sim B(n,q)\)で\(Z = X+Y\)\(E = E+E = mp+nq\)\(V = V+V = mp(1-p)...

\(X_i,Y_i\)は互いに独立の正規分布に従うため、\(D_i\)は、平均が\(E\)\( = (\mu_i+\theta) -\mu_i = \theta\)分散が\(V\)\( = V + V = 2\sigma^2\)の正規分布に...

\(f(x) = \displaystyle \frac{d}{dx}F(x)\)\(\displaystyle =\left \{ \begin{array}{} \frac{1}{\gamma}x^{-\frac{1}{\gamma}-...

\(E\)\(\displaystyle E = \sum _{k=0}^\infty kP(X=k)\)\(\displaystyle = \sum _{k=1}^\infty kP(X=k)\) (\(k=0\)の時は\(0\)のため除...

\(F_1(u)=P(U \leq u)\)\(\displaystyle = \int^{1}_{-1} P(U \leq u, V=v) \partial v\)\(\displaystyle = \int^{1}_{-1} \frac...

独立な時、\(P(A \cap B) = P(A)P(B)\)\(,P(A \cap B \cap C) = P(A)P(B)P(C)\)なので\( \displaystyle P(A \cap B) = \frac{9}{16}\)\(,...