private void gen18()
{
double part1, part2, part3, part4, part5, part6, Mn, ME, Dn, DE, MEn, DEn;
part1 = r.Next(1, 8);
part2 = r.Next(1, 10 - (int)part1);
part3 = 10 - part1 - part2;
part4 = r.Next(0, (int)part1) / 10d;
part1 = Math.Abs(part1 / 10d - part4);
part5 = r.Next(0, (int)part2) / 10d;
part2 = Math.Abs(part2 / 10d - part5);
part6 = r.Next(0, (int)part3) / 10d;
part3 = Math.Abs(part3 / 10d - part6);
paragraph = document.InsertParagraph();
paragraph.AppendLine("18. ").Font(font).FontSize(12).Bold().Alignment = Alignment.left;
paragraph.Append("Дана таблица распределения вероятностей двумерной случайной величины (y,x)").Font(font).FontSize(12);
Table table = document.AddTable(3, 4);
table.Alignment = Alignment.center;
table.SetColumnWidth(0, 40);
table.SetColumnWidth(1, 40);
table.SetColumnWidth(2, 40);
table.SetColumnWidth(3, 40);
table.Rows[0].Cells[0].Paragraphs[0].Append("y/x").Alignment = Alignment.center;
table.Rows[0].Cells[1].Paragraphs[0].Append("-1").Alignment = Alignment.center;
table.Rows[0].Cells[2].Paragraphs[0].Append("0").Alignment = Alignment.center;
table.Rows[0].Cells[3].Paragraphs[0].Append("1").Alignment = Alignment.center;
table.Rows[1].Cells[0].Paragraphs[0].Append("0").Alignment = Alignment.center;
table.Rows[2].Cells[0].Paragraphs[0].Append("1").Alignment = Alignment.center;
table.Rows[1].Cells[1].Paragraphs[0].Append(part1.ToString()).Alignment = Alignment.center;
table.Rows[1].Cells[2].Paragraphs[0].Append(part2.ToString()).Alignment = Alignment.center;
table.Rows[1].Cells[3].Paragraphs[0].Append(part3.ToString()).Alignment = Alignment.center;
table.Rows[2].Cells[1].Paragraphs[0].Append(part4.ToString()).Alignment = Alignment.center;
table.Rows[2].Cells[2].Paragraphs[0].Append(part5.ToString()).Alignment = Alignment.center;
table.Rows[2].Cells[3].Paragraphs[0].Append(part6.ToString()).Alignment = Alignment.center;
paragraph = document.InsertParagraph();
paragraph.InsertTableBeforeSelf(table);
paragraph.Append("Найти М(y), М(x), М(yx), D(y), D(x), D(yx).").Font(font).FontSize(12);
ME = part4 + part5 + part6;
DE = part4 + part5 + part6 - ME * ME;
Mn = (part1 + part4) * (-1) + part3 + part6;
Dn = (part1 + part4) + part3 + part6 - Mn * Mn;
MEn = 1d * (-1d) * part4 + 1d * 1d * part6;
DEn = 1d * 1d * part4 + 1d * 1d * part6 - MEn * MEn;
allresult[variantIterator] += "\n18. М(y)= " + ME.ToString() +
"\n D(y)= " + doubleNormalize(DE.ToString()) +
"\n М(x)= " + doubleNormalize(Mn.ToString()) +
"\n D(x)= " + doubleNormalize(Dn.ToString()) +
"\n М(yx)= " + doubleNormalize(MEn.ToString()) +
"\n D(yx)= " + doubleNormalize(DEn.ToString()) + ". ";
}
private void gen13_14()
{
string[] f1 = new string[] { "-π/2", "-π/3", "-π/4", "-π/6", "0" };
string[] f2 = new string[] { "π/2", "π/3", "π/4", "π/6" };
int part1 = randInt(0, 4);
int part2 = randInt(0, 3);
paragraph = document.InsertParagraph();
paragraph.AppendLine("13. ").Font(font).FontSize(12).Bold().Alignment = Alignment.left;
paragraph.Append("Задана плотность распределения непрерывной случайной величины x:"
+ "\n p(х)=K*cos(x), ∀x ∈ (" + f1[part1] + " ; " + f2[part2] + "]\n p(х)=0, ∀x ∉ (" + f1[part1] + " ; " + f2[part2] + "]\nНайти K и функцию распределения F(x).").Font(font).FontSize(12);
string[,] kresultm = new string[, ] {
{ "1/2", "(-2√3 + 4)", "(√2 +2)", "2/3" },
{ "(4-2√3)", "√3/3", "(-2√2 + 2√3)", "(-1+√3)" },
{ "(2-√2)", "(2√3-2√2)", "√2/2", "(-2+2√2)" },
{ "2/3", "(√3 -1)", "(2√2-2)", "1" },
{ "1", "2√3/3", "√2", "2" }
};
string kresult = kresultm[part1, part2];
string fresult = "\n p(х)=0,при x≤" + f1[part1] +
"\n p(х)=" + kresult + "*sin(x),при " + f1[part1] + " < x ≤ " + f2[part2] +
"\n p(х)=1,при x > " + f2[part2];
allresult[variantIterator] += "\n13. K= " + kresult.ToString() + fresult + "; ";
double ME, DE, q;
paragraph = document.InsertParagraph();
paragraph.AppendLine("14. ").Font(font).FontSize(12).Bold().Alignment = Alignment.left;
paragraph.Append("X - непрерывная случайная величина примера 13. Найти М(X), D(X), σ(X).").Font(font).FontSize(12);
double[] f1num = new double[] { -Math.PI / 2d, -Math.PI / 3d, -Math.PI / 4d, -Math.PI / 6d, 0d };
double[] f2num = new double[] { Math.PI / 2d, Math.PI / 3d, Math.PI / 4d, Math.PI / 6d };
double[,] knum = new double[, ] {
{ 1d / 2d, -2d * (double)Math.Sqrt(3d) + 4d, (double)Math.Sqrt(2d) + 2d, 2d / 3d },
{ 4d - 2d * (double)Math.Sqrt(3d), (double)Math.Sqrt(3d) / 3d, -2d * (double)Math.Sqrt(2d) + 2d * (double)Math.Sqrt(3d), -1d * (double)Math.Sqrt(3d) },
{ 2d - (double)Math.Sqrt(2d), 2d * (double)Math.Sqrt(3d) - 2d * (double)Math.Sqrt(2d), (double)Math.Sqrt(2d) / 2d, -2d + 2d * (double)Math.Sqrt(2d) },
{ 2d / 3d, (double)Math.Sqrt(3d) - 1d, 2d * (double)Math.Sqrt(2d) - 2d, 1d },
{ 1d, 2d * (double)Math.Sqrt(3d) / 3d, (double)Math.Sqrt(2d), 2d }
};
ME = knum[part1, part2] * (f2num[part2] * Math.Sin(f2num[part2]) + Math.Cos(f2num[part2]) - (f1num[part1] * Math.Sin(f1num[part1]) + Math.Cos(f1num[part1])));
DE = knum[part1, part2] * (f2num[part2] * f2num[part2] * Math.Sin(f2num[part2]) + 2d * f2num[part2] * Math.Cos(f2num[part2]) + 2d * Math.Sin(f2num[part2]) - (f1num[part1] * f2num[part1] * Math.Sin(f1num[part1]) + 2d * f1num[part1] * Math.Cos(f1num[part1]) + 2d * Math.Sin(f1num[part1]))) - ME * ME;
q = Math.Sqrt(DE);
allresult[variantIterator] +=
"\n14. М(X)= " + doubleNormalize(ME.ToString()) +
"\n D(X)= " + doubleNormalize(DE.ToString()) +
"\n σ(X)= " + doubleNormalize(q.ToString()) + ";";
}
private void gen11_12()
{
double part1, part2, part3, part4, part5;
part1 = r.Next(1, 8);
part2 = r.Next(1, 10 - (int)part1);
part3 = 10 - part1 - part2;
part4 = r.Next(0, (int)part1) / 10d;
part1 = Math.Abs(part1 / 10d - part4);
part5 = r.Next(0, (int)part2) / 10d;
part2 = Math.Abs(part2 / 10d - part5);
part3 /= 10d;
paragraph = document.InsertParagraph();
paragraph.AppendLine("11. ").Font(font).FontSize(12).Bold().Alignment = Alignment.left;
paragraph.Append("Случайная величина X имеет распределения вероятностей, представленное таблицей:").Font(font).FontSize(12);
Table table = document.AddTable(2, 6);
table.Alignment = Alignment.center;
table.SetColumnWidth(0, 40);
table.SetColumnWidth(1, 40);
table.SetColumnWidth(2, 40);
table.SetColumnWidth(3, 40);
table.SetColumnWidth(4, 40);
table.SetColumnWidth(5, 40);
table.Rows[0].Cells[0].Paragraphs[0].Append("X").Alignment = Alignment.center;
table.Rows[1].Cells[0].Paragraphs[0].Append("P(x)").Alignment = Alignment.center;
table.Rows[0].Cells[1].Paragraphs[0].Append("-1").Alignment = Alignment.center;
table.Rows[0].Cells[2].Paragraphs[0].Append("0").Alignment = Alignment.center;
table.Rows[0].Cells[3].Paragraphs[0].Append("1").Alignment = Alignment.center;
table.Rows[0].Cells[4].Paragraphs[0].Append("2").Alignment = Alignment.center;
table.Rows[0].Cells[5].Paragraphs[0].Append("3").Alignment = Alignment.center;
table.Rows[1].Cells[1].Paragraphs[0].Append(part1.ToString()).Alignment = Alignment.center;
table.Rows[1].Cells[2].Paragraphs[0].Append(part2.ToString()).Alignment = Alignment.center;
table.Rows[1].Cells[3].Paragraphs[0].Append(part3.ToString()).Alignment = Alignment.center;
table.Rows[1].Cells[4].Paragraphs[0].Append(part4.ToString()).Alignment = Alignment.center;
table.Rows[1].Cells[5].Paragraphs[0].Append(part5.ToString()).Alignment = Alignment.center;
paragraph = document.InsertParagraph();
paragraph.InsertTableBeforeSelf(table);
paragraph.Append("Построить многоугольник распределения и найти функцию распределения F(x).").Font(font).FontSize(12);
string resultf = "p(х)=0, при x≤-1\n p(х)=" + part1.ToString() + ", при -1<x≤0\n" +
" p(х)=" + (part1 + part2).ToString() + ", при 0<x≤1\n" +
" p(х)=" + (part1 + part2 + part3).ToString() + ", при 1<x≤2\n" +
" p(х)=" + (part1 + part2 + part3 + part4).ToString() + ", при 2<x≤3\n" +
" p(х)=" + (part1 + part2 + part3 + part4 + part5).ToString() + ", при x>3";
allresult[variantIterator] += "\n11. " + resultf + ";";
paragraph = document.InsertParagraph();
paragraph.AppendLine("12. ").Font(font).FontSize(12).Bold().Alignment = Alignment.left;
paragraph.Append("Найти М(X), D(X), σ(X) случайной величины X примера 11.").Font(font).FontSize(12);
double ME, DE, q;
ME = -1 * part1 + 0 * part2 + 1 * part3 + 2 * part4 + 3 * part5;
DE = 1 * part1 + 0 * part2 + 1 * part3 + 4 * part4 + 9 * part5 - ME * ME;
q = Math.Sqrt(DE);
allresult[variantIterator] += "\n12. М(X)=" + doubleNormalize(ME.ToString()) + "\n D(X)=" + doubleNormalize(DE.ToString()) + "\n σ(X)= " + doubleNormalize(q.ToString()) + "; ";
}
