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About 79 results
  • 1: Системи ймовірності
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/01%3A_%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B8_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D1%96
  • 4.2: MATLAB та незалежні класи
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/04%3A_%D0%9D%D0%B5%D0%B7%D0%B0%D0%BB%D0%B5%D0%B6%D0%BD%D1%96%D1%81%D1%82%D1%8C_%D0%BF%D0%BE%D0%B4%D1%96%D0%B9/4.02%3A_MATLAB_%D1%82%D0%B0_%D0%BD%D0%B5%D0%B7%D0%B0%D0%BB%D0%B5%D0%B6%D0%BD%D1%96_%D0%BA%D0%BB%D0%B0%D1%81%D0%B8
    >> p = 0.01*[13 37 12 56 33 71 22 43 57 31]; >> pa = p([1 3 4 7]); % Selection of probabilities for A >> pb = p([2 5 6 8]); % Selection of probabilities for B >> pma = minprob(pa); % Minterm probabili...>> p = 0.01*[13 37 12 56 33 71 22 43 57 31]; >> pa = p([1 3 4 7]); % Selection of probabilities for A >> pb = p([2 5 6 8]); % Selection of probabilities for B >> pma = minprob(pa); % Minterm probabilities for calculating P(A) >> pmb = minprob(pb); % Minterm probabilities for calculating P(B) >> minvec4; >> a = A|(B&(C|Dc)); % A corresponds to E1, B to E3, C to E4, D to E7 >> PA = a*pma' PA = 0.2243 >> b = A&(Bc|(C&D)); % A corresponds to E2, B to E5, C to E6, D to E8 >> PB = b*pmb' PB = 0.2852 …
  • 1.3: Тлумачення
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/01%3A_%D0%A1%D0%B8%D1%81%D1%82%D0%B5%D0%BC%D0%B8_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D1%96/1.03%3A_%D0%A2%D0%BB%D1%83%D0%BC%D0%B0%D1%87%D0%B5%D0%BD%D0%BD%D1%8F
    (IF5):\(I_{A \cup B} = I_A + I_B - I_A I_B = \text{min }{I_A, I_B}\) (правило максимуму поширюється на будь-який клас) Правило максимуму випливає з того факту, що\(\omega\) знаходиться в об'єднанні, я...(IF5):\(I_{A \cup B} = I_A + I_B - I_A I_B = \text{min }{I_A, I_B}\) (правило максимуму поширюється на будь-який клас) Правило максимуму випливає з того факту, що\(\omega\) знаходиться в об'єднанні, якщо воно є в будь-якій одній або декількох подіях в об'єднанні, якщо будь-яка одна або кілька окремих індикаторних функцій має значення один iff максимальний один.
  • 15.1: Випадковий вибір
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/15%3A_%D0%92%D0%B8%D0%BF%D0%B0%D0%B4%D0%BA%D0%BE%D0%B2%D0%B8%D0%B9_%D0%B2%D0%B8%D0%B1%D1%96%D1%80/15.01%3A_%D0%92%D0%B8%D0%BF%D0%B0%D0%B4%D0%BA%D0%BE%D0%B2%D0%B8%D0%B9_%D0%B2%D0%B8%D0%B1%D1%96%D1%80
    gN = (1/3)*[0 1 1 1]; % Note zero coefficient for missing zero power gY = 0.1*[5 4 1]; % All powers 0 thru 2 have positive coefficients gend Do not forget zero coefficients for missing powers Enter th...gN = (1/3)*[0 1 1 1]; % Note zero coefficient for missing zero power gY = 0.1*[5 4 1]; % All powers 0 thru 2 have positive coefficients gend Do not forget zero coefficients for missing powers Enter the gen fn COEFFICIENTS for gN gN % Coefficient matrix named gN Enter the gen fn COEFFICIENTS for gY gY % Coefficient matrix named gY Results are in N, PN, Y, PY, D, PD, P May use jcalc or jcalcf on N, D, P To view distribution for D, call for gD disp(gD) % Optional display of complete distribution 0…
  • 2.2: Розрахунки Мінтермс та MATLAB
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/02%3A_%D0%9C%D1%96%D0%BD%D1%82%D0%B5%D1%80%D0%BC%D1%96%D0%BD%D0%BD%D0%B8%D0%B9_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7/2.02%3A_%D0%A0%D0%BE%D0%B7%D1%80%D0%B0%D1%85%D1%83%D0%BD%D0%BA%D0%B8_%D0%9C%D1%96%D0%BD%D1%82%D0%B5%D1%80%D0%BC%D1%81_%D1%82%D0%B0_MATLAB
    \(E = A(B \cup C^c) \cup A^c (B \cup C^c)^c \cup A^c (B \cup C^c)^c \sim\)[0 1 0 0 1 1] і\(F = A^c B^c \cup AC \sim\) [1 1 0 0 0 1] Розглянемо\(E = A (B \cup C^c) \cup A^c (B \cup C^c)^c\) і\(F = A^c ...\(E = A(B \cup C^c) \cup A^c (B \cup C^c)^c \cup A^c (B \cup C^c)^c \sim\)[0 1 0 0 1 1] і\(F = A^c B^c \cup AC \sim\) [1 1 0 0 0 1] Розглянемо\(E = A (B \cup C^c) \cup A^c (B \cup C^c)^c\) і\(F = A^c B^c \cup AC\) приклад вище, і припустимо, що відповідні мінтермальні ймовірності є
  • Передня матерія
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/00%3A_%D0%9F%D0%B5%D1%80%D0%B5%D0%B4%D0%BD%D1%8F_%D0%BC%D0%B0%D1%82%D0%B5%D1%80%D1%96%D1%8F
  • 4: Незалежність подій
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/04%3A_%D0%9D%D0%B5%D0%B7%D0%B0%D0%BB%D0%B5%D0%B6%D0%BD%D1%96%D1%81%D1%82%D1%8C_%D0%BF%D0%BE%D0%B4%D1%96%D0%B9
  • 7.1: Функції розподілу та щільності
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/07%3A_%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%97_%D1%80%D0%BE%D0%B7%D0%BF%D0%BE%D0%B4%D1%96%D0%BB%D1%83_%D1%82%D0%B0_%D1%89%D1%96%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%96/7.01%3A_%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%97_%D1%80%D0%BE%D0%B7%D0%BF%D0%BE%D0%B4%D1%96%D0%BB%D1%83_%D1%82%D0%B0_%D1%89%D1%96%D0%BB%D1%8C%D0%BD%D0%BE%D1%81%D1%82%D1%96
    Якщо точка\(t\) наближається\(t_0\) зліва, інтервал не включає масу ймовірності до тих пір,\(t_0\) поки не\(t\) досягне цього значення, в цей момент сума в або ліворуч від t збільшується («стрибає») н...Якщо точка\(t\) наближається\(t_0\) зліва, інтервал не включає масу ймовірності до тих пір,\(t_0\) поки не\(t\) досягне цього значення, в цей момент сума в або ліворуч від t збільшується («стрибає») на суму\(p_0\); з іншого боку, якщо\(t\) наближається\(t_0\) справа, інтервал включає масу\(p_0\) аж до і в тому числі\(t_0\), але падає відразу, як\(t\) рухається зліва від\(t_0\). \(P(X > t + h|X > t) = P(X > t + h)/P(X > t) = e^{-\lambda (t+ h)}/e^{-\lambda t} = e^{-\lambda h} = P(X > h)\)
  • 12.4: Задачі про дисперсію, коваріацію, лінійну регресію
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/12%3A_%D0%B4%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D1%96%D1%8F%2C_%D0%BA%D0%BE%D0%B2%D0%B0%D1%80%D1%96%D0%B0%D1%86%D1%96%D1%8F_%D1%82%D0%B0_%D0%BB%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D0%B0_%D1%80%D0%B5%D0%B3%D1%80%D0%B5%D1%81%D1%96%D1%8F/12.04%3A_%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D1%96_%D0%BF%D1%80%D0%BE_%D0%B4%D0%B8%D1%81%D0%BF%D0%B5%D1%80%D1%81%D1%96%D1%8E%2C_%D0%BA%D0%BE%D0%B2%D0%B0%D1%80%D1%96%D0%B0%D1%86%D1%96%D1%8E%2C_%D0%BB%D1%96%D0%BD%D1%96%D0%B9%D0%BD%D1%83_%D1%80%D0%B5%D0%B3%D1%80%D0%B5%D1%81%D1%96%D1%8E
    x = [-5 -1 3 4 7]; px = 0.01*[15 20 30 25 10]; EX = dot(x,px) % Use of properties EX = 1.6500 VX = dot(x.^2,px) - EX^2 VX = 12.8275 EW = (3 - 4+ 2)*EX EW = 1.6500 VW = (3^2 + 4^2 + 2^2)*VX VW = 371.99...x = [-5 -1 3 4 7]; px = 0.01*[15 20 30 25 10]; EX = dot(x,px) % Use of properties EX = 1.6500 VX = dot(x.^2,px) - EX^2 VX = 12.8275 EW = (3 - 4+ 2)*EX EW = 1.6500 VW = (3^2 + 4^2 + 2^2)*VX VW = 371.9975 icalc % Iterated use of icalc Enter row matrix of X-values x Enter row matrix of Y-values x Enter X probabilities px Enter Y probabilities px Use array operations on matrices X, Y, PX, PY, t, u, and P G = 3*t - 4*u; [R,PR] = csort(G,P); icalc Enter row matrix of X-values R Enter row matrix of Y-…
  • 10.1: Функції випадкової величини
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/10%3A_%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%97_%D0%B2%D0%B8%D0%BF%D0%B0%D0%B4%D0%BA%D0%BE%D0%B2%D0%B8%D1%85_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD/10.01%3A_%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%96%D1%97_%D0%B2%D0%B8%D0%BF%D0%B0%D0%B4%D0%BA%D0%BE%D0%B2%D0%BE%D1%97_%D0%B2%D0%B5%D0%BB%D0%B8%D1%87%D0%B8%D0%BD%D0%B8
    X = -5:10; % Values of X PX = ibinom(15,0.6,0:15); % Probabilities for X G = (X + 6).*(X - 1).*(X - 8); % Array operations on X matrix to get G = g(X) M = (G > - 100)&(G < 130); % Relational and logic...X = -5:10; % Values of X PX = ibinom(15,0.6,0:15); % Probabilities for X G = (X + 6).*(X - 1).*(X - 8); % Array operations on X matrix to get G = g(X) M = (G > - 100)&(G < 130); % Relational and logical operations on G PM = M*PX' % Sum of probabilities for selected values PM = 0.4800 disp([X;G;M;PX]') % Display of various matrices (as columns) -5.0000 78.0000 1.0000 0.0000 -4.0000 120.0000 1.0000 0.0000 -3.0000 132.0000 0 0.0003 -2.0000 120.0000 1.0000 0.0016 -1.0000 90.0000 1.0000 0.0074 0 48.…
  • 11.3: Задачі математичного очікування
    https://ukrayinska.libretexts.org/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D0%BE%D1%81%D1%82%D0%B5%D0%B9/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%B9%D0%BC%D0%BE%D0%B2%D1%96%D1%80%D0%BD%D1%96%D1%81%D1%82%D1%8C_(Pfeiffer)/11%3A_%D0%A1%D1%82%D0%BE%D1%80%D1%96%D0%BD%D0%BA%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%B8%D1%85_%D0%BE%D1%87%D1%96%D0%BA%D1%83%D0%B2%D0%B0%D0%BD%D1%8C/11.03%3A_%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D1%96_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BD%D0%BE%D0%B3%D0%BE_%D0%BE%D1%87%D1%96%D0%BA%D1%83%D0%B2%D0%B0%D0%BD%D0%BD%D1%8F
    x = [-5 -1 3 4 7]; px = 0.01*[15 20 30 25 10]; icalc Enter row matrix of X-values x Enter row matrix of Y-values x Enter X probabilities px Enter Y probabilities px Use array operations on matrices X,...x = [-5 -1 3 4 7]; px = 0.01*[15 20 30 25 10]; icalc Enter row matrix of X-values x Enter row matrix of Y-values x Enter X probabilities px Enter Y probabilities px Use array operations on matrices X, Y, PX, PY, t, u, and P G = 3*t - 4*u [R,PR] = csort(G,P); icalc Enter row matrix of X-values R Enter row matrix of Y-values x Enter X probabilities PR Enter Y probabilities px Use array operations on matrices X, Y, PX, PY, t, u, and P H = t + 2*u; EH = total(H.*P) EH = 1.6500 [W,PW] = csort(H,P); …