BIẾN NGẪU NHIÊN VÀ QUY LUẬT PHÂN PHỐI XÁC SUẤT

1 8/27/2014 Chương BIẾN NGẪU NHIÊN VÀ QUY LUẬT PHÂN PHỐI XÁC SUẤT Chương 8/27/2014 Nội dung Sausage 5.8% 900000 800000 800000 600000 500000 400000 Mushroom 16.2% Plain 32.5% Scatterplot of Listing vs IncomePC 900000 Scatterplot of Listing vs IncomePC Normal - 95% CI 900000 Mean StDev N AD P-Value 95 90 500000 400000 200000 100000 15000 800000 700000 60 50 40 30 20000 22500 25000 IncomePC 27500 30000 32500 e  mc   200000 100000 15000 400000 600000 Listing 800000 1000000 17500 20000 22500 25000 IncomePC 27500 Mean StDev N 369687 156865 51 80 200000 Normal 10 300000 Marginal Plot of Listing vs IncomePC Empirical CDF of Listing 100 12 500000 400000 10 17500 Histogram of Listing 14 600000 70 20 300000 200000 369687 156865 51 0.994 0.012 80 600000 300000 100000 Probability Plot of Listing 99 700000 700000 Listing Pepper and Onion 7.3% Boxplot of Listing Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball 30000 32500 1000000 60 800000 40 Listing Pepperoni 21.8% Percent Meatball Garlic 5.0% 2.3% Frequency Pie Chart of Percent vs Type Mushroom and Onion 9.2% Listing Percent Các loại biến ngẫu nhiên (bnn) Quy luật phân phối xs bnn rời rạc liên tục Các tham số đặc trưng bnn cách tính tốn Listing 20 600000 400000 0 200000 300000 400000 500000 600000 Listing 700000 800000 900000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing 200000 15000 20000 25000 IncomePC 30000 Chương 8/27/2014 Định nghĩa phân loại bnn (1) ĐN: Biến nn đại lượng mà kết phép thử nhận giá trị có tùy thuộc vào nhân tố ngẫu nhiên  VD1: Tung xúc xắc mặt Gọi X số chấm xuất => X bnn  VD2: Năng suất lúa vùng khác => biến ngẫu nhiên  600000 500000 400000 Mushroom 16.2% Plain 32.5% Scatterplot of Listing vs IncomePC Normal - 95% CI 900000 Mean StDev N AD P-Value 95 700000 90 500000 400000 200000 100000 15000 800000 700000 60 50 40 30 20000 22500 25000 IncomePC 27500 30000 32500 e  mc   200000 100000 15000 400000 600000 Listing 800000 1000000 17500 20000 22500 25000 IncomePC 27500 Mean StDev N 369687 156865 51 80 200000 Normal 10 300000 Marginal Plot of Listing vs IncomePC Empirical CDF of Listing 100 12 500000 400000 10 17500 Histogram of Listing 14 600000 70 20 300000 200000 369687 156865 51 0.994 0.012 80 600000 300000 100000 Probability Plot of Listing 99 30000 32500 1000000 60 800000 40 Listing 800000 800000 Percent 900000 Frequency Sausage 5.8% Scatterplot of Listing vs IncomePC 900000 700000 Listing Pepper and Onion 7.3% Boxplot of Listing Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball Listing Pepperoni 21.8% Listing Meatball Garlic 5.0% 2.3% Percent Pie Chart of Percent vs Type Mushroom and Onion 9.2% 20 600000 400000 0 200000 300000 400000 500000 600000 Listing 700000 800000 900000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing 200000 15000 20000 25000 IncomePC 30000 Chương 8/27/2014 Định nghĩa phân loại bnn (2)  Bnn đgl liên tục giá trị có lấp đầy khoảng trục số VD2: Năng suất lúa vụ mùa vùng khác => bnn liên tục Pepperoni 21.8% Sausage 5.8% 900000 800000 800000 600000 500000 400000 Mushroom 16.2% Plain 32.5% Scatterplot of Listing vs IncomePC 900000 Scatterplot of Listing vs IncomePC Normal - 95% CI 900000 Mean StDev N AD P-Value 95 90 500000 400000 200000 100000 15000 800000 700000 60 50 40 30 20000 22500 25000 IncomePC 27500 30000 32500 e  mc   200000 100000 15000 400000 600000 Listing 800000 1000000 17500 20000 22500 25000 IncomePC 27500 Mean StDev N 369687 156865 51 80 200000 Normal 10 300000 Marginal Plot of Listing vs IncomePC Empirical CDF of Listing 100 12 500000 400000 10 17500 Histogram of Listing 14 600000 70 20 300000 200000 369687 156865 51 0.994 0.012 80 600000 300000 100000 Probability Plot of Listing 99 700000 700000 Listing Pepper and Onion 7.3% Boxplot of Listing Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball 30000 32500 1000000 60 800000 40 Listing Meatball Garlic 5.0% 2.3% Percent Pie Chart of Percent vs Type Mushroom and Onion 9.2% Frequency  Listing  VD1: Tung xúc xắc mặt Gọi X số chấm xuất => X bnn rời rạc Percent  Có loại bnn: rời rạc liên tục Bnn đgl rời rạc giá trị có lập nên tập hợp hữu hạn đếm Listing  20 600000 400000 0 200000 300000 400000 500000 600000 Listing 700000 800000 900000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing 200000 15000 20000 25000 IncomePC 30000 Chương 8/27/2014 Quy luật PPXS BNN (1) X x1 x2 … xn P p1 p2 … pn Sausage 5.8% 900000 800000 800000 600000 500000 400000 Mushroom 16.2% Plain 32.5% Scatterplot of Listing vs IncomePC 900000 Scatterplot of Listing vs IncomePC Normal - 95% CI 900000 Mean StDev N AD P-Value 95 90 500000 400000 200000 100000 15000 800000 700000 60 50 40 30 20000 22500 25000 IncomePC 27500 30000 32500 e  mc   200000 100000 15000 400000 600000 Listing 800000 1000000 17500 20000 22500 25000 IncomePC 27500 Mean StDev N 369687 156865 51 80 200000 Normal 10 300000 Marginal Plot of Listing vs IncomePC Empirical CDF of Listing 100 12 500000 400000 10 17500 Histogram of Listing 14 600000 70 20 300000 200000 369687 156865 51 0.994 0.012 80 600000 300000 100000 Probability Plot of Listing 99 700000 700000 Listing Pepper and Onion 7.3% Boxplot of Listing Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball 30000 32500 1000000 60 800000 40 Listing Pepperoni 21.8% Percent Meatball Garlic 5.0% 2.3% Listing Pie Chart of Percent vs Type Mushroom and Onion 9.2% ≤ pi ≤ ∑ pi = Frequency Lưu ý: Percent  QL PPXS BNN tương ứng các trị có xs tương ứng với giá trị Listing  20 600000 400000 0 200000 300000 400000 500000 600000 Listing 700000 800000 900000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing 200000 15000 20000 25000 IncomePC 30000 Chương 8/27/2014 Quy luật PPXS BNN (2) Ví dụ: Gieo xúc xắc Gọi X “số chấm xuất hiện” Tìm quy luật ppxs X  Vì X bnn rời rạc => lập bảng ppxs X  X P 1/6 1/6 1/6 1/6 1/6 1/6 600000 500000 400000 Mushroom 16.2% Plain 32.5% Scatterplot of Listing vs IncomePC Normal - 95% CI 900000 Mean StDev N AD P-Value 95 700000 90 500000 400000 200000 100000 15000 800000 700000 60 50 40 30 20000 22500 25000 IncomePC 27500 30000 32500 e  mc   200000 100000 15000 400000 600000 Listing 800000 1000000 17500 20000 22500 25000 IncomePC 27500 Mean StDev N 369687 156865 51 80 200000 Normal 10 300000 Marginal Plot of Listing vs IncomePC Empirical CDF of Listing 100 12 500000 400000 10 17500 Histogram of Listing 14 600000 70 20 300000 200000 369687 156865 51 0.994 0.012 80 600000 300000 100000 Probability Plot of Listing 99 30000 32500 1000000 60 800000 40 Listing 800000 800000 Percent 900000 Frequency Sausage 5.8% Scatterplot of Listing vs IncomePC 900000 700000 Listing Pepper and Onion 7.3% Boxplot of Listing Category Pepperoni Plain Mushroom Sausage Pepper and Onion Mushroom and Onion Garlic Meatball Listing Pepperoni 21.8% Listing Meatball Garlic 5.0% 2.3% Percent Pie Chart of Percent vs Type Mushroom and Onion 9.2% 20 600000 400000 0 200000 300000 400000 500000 600000 Listing 700000 800000 900000 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 20 30 40 50 60 70 80 90 Listing 200000 15000 20000 25000 IncomePC 30000 Chương 8/27/2014 Quy luật PPXS BNN (3)  Các hình thức mơ tả QLPPXS BNN Bảng PPXS Hàm phân bố XS Hàm mật độ XS Hàm phân bố XS BNN X, ký hiệu F(x), XS để X nhận giá trị nhỏ x, x R F(x) = P (X