Discrete and Continuous Random Variables

/**
 * Fintech Math Bootcamp · Lesson 056 of 120
 * Discrete and Continuous Random Variables
 * Module 06: Probability and Random Variables
 *
 * Scenario: Distinguishing uncertain counts from uncertain amounts
 * Rule:     a random variable maps outcomes to numbers
 *
 * Try it:   Must an expected value be one of the possible individual outcomes?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/discrete-and-continuous-random-variables/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

export function lesson056() {
  const losses=[0,100,500], probabilities=[.90,.08,.02];
  const result = {positiveLossProbability: probabilities[1]+probabilities[2],
    expectedLoss: losses.reduce((s,l,i)=>s+l*probabilities[i],0)};
  return result;
}

export const checkedResult = {"positiveLossProbability":0.1,"expectedLoss":18};

// Run this file directly: npx tsx lessons/06-probability-and-random-variables/056-discrete-and-continuous-random-variables.ts
if (process.argv[1] && import.meta.url.endsWith(process.argv[1].replace(/\\/g, "/").split("/").pop()!)) {
  console.log(JSON.stringify(lesson056(), null, 2));
}

# Fintech Math Bootcamp · Lesson 056 of 120
# Discrete and Continuous Random Variables
# Module 06: Probability and Random Variables
#
# Scenario: Distinguishing uncertain counts from uncertain amounts
# Rule:     a random variable maps outcomes to numbers
#
# Try it:   Must an expected value be one of the possible individual outcomes?
#
# Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/discrete-and-continuous-random-variables/
# Free course:    https://courses.thefintechbuilder.com
# Synthetic teaching example, not financial advice or a production library.

import json


def lesson056() -> dict:
    losses, probabilities = [0, 100, 500], [0.90, 0.08, 0.02]
    return {
        "positiveLossProbability": probabilities[1] + probabilities[2],
        "expectedLoss": sum(loss * p for loss, p in zip(losses, probabilities)),
    }


if __name__ == "__main__":
    print(json.dumps(lesson056(), indent=2))

/**
 * Fintech Math Bootcamp · Lesson 056 of 120
 * Discrete and Continuous Random Variables
 * Module 06: Probability and Random Variables
 *
 * Scenario: Distinguishing uncertain counts from uncertain amounts
 * Rule:     a random variable maps outcomes to numbers
 *
 * Try it:   Must an expected value be one of the possible individual outcomes?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/discrete-and-continuous-random-variables/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

import java.util.ArrayList;
import java.util.LinkedHashMap;
import java.util.List;
import java.util.Map;

public class Main {
    static Map<String, Object> lesson056() {
        double[] losses = {0, 100, 500};
        double[] probabilities = {0.90, 0.08, 0.02};
        double expectedLoss = 0;
        for (int i = 0; i < losses.length; i++) expectedLoss += losses[i] * probabilities[i];
        Map<String, Object> result = new LinkedHashMap<String, Object>();
        result.put("positiveLossProbability", probabilities[1] + probabilities[2]);
        result.put("expectedLoss", expectedLoss);
        return result;
    }

    public static void main(String[] args) {
        System.out.println(toJson(lesson056(), ""));
    }

    // --- Minimal JSON printer: maps keep insertion order, 2-space indent. ---

    static String toJson(Object value, String indent) {
        if (value == null) return "null";
        if (value instanceof String) return "\"" + value + "\"";
        if (value instanceof Double) return formatNumber((Double) value);
        if (value instanceof Number) return value.toString();
        if (value instanceof double[]) {
            List<Object> items = new ArrayList<Object>();
            for (double v : (double[]) value) items.add(v);
            return toJson(items, indent);
        }
        String inner = indent + "  ";
        StringBuilder sb = new StringBuilder();
        if (value instanceof Map) {
            Map<?, ?> map = (Map<?, ?>) value;
            if (map.isEmpty()) return "{}";
            sb.append("{\n");
            int i = 0;
            for (Map.Entry<?, ?> entry : map.entrySet()) {
                sb.append(inner).append('"').append(entry.getKey()).append("\": ")
                  .append(toJson(entry.getValue(), inner))
                  .append(++i < map.size() ? ",\n" : "\n");
            }
            return sb.append(indent).append('}').toString();
        }
        List<?> list = (List<?>) value;
        if (list.isEmpty()) return "[]";
        sb.append("[\n");
        for (int i = 0; i < list.size(); i++) {
            sb.append(inner).append(toJson(list.get(i), inner))
              .append(i + 1 < list.size() ? ",\n" : "\n");
        }
        return sb.append(indent).append(']').toString();
    }

    static String formatNumber(double v) {
        if (Double.isNaN(v) || Double.isInfinite(v)) return "null";
        if (v == Math.rint(v) && Math.abs(v) < 1e15) return Long.toString((long) v);
        return Double.toString(v);
    }
}

// Fintech Math Bootcamp · Lesson 056 of 120
// Discrete and Continuous Random Variables
// Module 06: Probability and Random Variables
//
// Scenario: Distinguishing uncertain counts from uncertain amounts
// Rule:     a random variable maps outcomes to numbers
//
// Try it:   Must an expected value be one of the possible individual outcomes?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/discrete-and-continuous-random-variables/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

package main

import (
	"encoding/json"
	"fmt"
)

// LossVariable summarizes a discrete loss: the chance of any loss and its expectation.
type LossVariable struct {
	PositiveLossProbability float64 `json:"positiveLossProbability"`
	ExpectedLoss            float64 `json:"expectedLoss"`
}

func lesson056() LossVariable {
	losses, probabilities := []float64{0, 100, 500}, []float64{0.90, 0.08, 0.02}
	expectedLoss := 0.0
	for i, loss := range losses {
		expectedLoss += loss * probabilities[i]
	}
	return LossVariable{
		PositiveLossProbability: probabilities[1] + probabilities[2],
		ExpectedLoss:            expectedLoss,
	}
}

func main() {
	out, _ := json.MarshalIndent(lesson056(), "", "  ")
	fmt.Println(string(out))
}

/**
 * Fintech Math Bootcamp · Lesson 056 of 120
 * Discrete and Continuous Random Variables
 * Module 06: Probability and Random Variables
 *
 * Scenario: Distinguishing uncertain counts from uncertain amounts
 * Rule:     a random variable maps outcomes to numbers
 *
 * Try it:   Must an expected value be one of the possible individual outcomes?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/discrete-and-continuous-random-variables/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

#include <charconv>
#include <cmath>
#include <iostream>
#include <string>
#include <utility>
#include <vector>

// --- Minimal JSON value and printer: objects keep insertion order, 2-space indent. ---

struct Json {
    enum class Kind { Null, Number, Text, Array, Object };
    Kind kind = Kind::Null;
    double number = 0;
    std::string text;
    std::vector<std::string> keys;  // object keys, parallel to items
    std::vector<Json> items;        // array elements or object values
};

Json num(double v) { Json j; j.kind = Json::Kind::Number; j.number = v; return j; }
Json str(const std::string& s) { Json j; j.kind = Json::Kind::Text; j.text = s; return j; }
Json arr(const std::vector<Json>& values) { Json j; j.kind = Json::Kind::Array; j.items = values; return j; }

Json arr(const std::vector<double>& values) {
    std::vector<Json> items;
    for (double v : values) items.push_back(num(v));
    return arr(items);
}

Json obj(const std::vector<std::pair<std::string, Json>>& fields) {
    Json j;
    j.kind = Json::Kind::Object;
    for (const auto& [key, value] : fields) { j.keys.push_back(key); j.items.push_back(value); }
    return j;
}

std::string formatNumber(double v) {
    if (!std::isfinite(v)) return "null";
    char buf[64];
    auto end = std::to_chars(buf, buf + sizeof buf, v).ptr;  // shortest round-trip form
    return std::string(buf, end);
}

void writeJson(std::ostream& out, const Json& j, const std::string& indent) {
    switch (j.kind) {
    case Json::Kind::Null: out << "null"; return;
    case Json::Kind::Number: out << formatNumber(j.number); return;
    case Json::Kind::Text: out << '"' << j.text << '"'; return;
    default: break;
    }
    bool isObject = j.kind == Json::Kind::Object;
    if (j.items.empty()) { out << (isObject ? "{}" : "[]"); return; }
    std::string inner = indent + "  ";
    out << (isObject ? "{\n" : "[\n");
    for (size_t i = 0; i < j.items.size(); ++i) {
        out << inner;
        if (isObject) out << '"' << j.keys[i] << "\": ";
        writeJson(out, j.items[i], inner);
        out << (i + 1 < j.items.size() ? ",\n" : "\n");
    }
    out << indent << (isObject ? '}' : ']');
}

// --- Lesson ---

Json lesson056() {
    const std::vector<double> losses = {0, 100, 500};
    const std::vector<double> probabilities = {0.90, 0.08, 0.02};
    double expectedLoss = 0;
    for (size_t i = 0; i < losses.size(); ++i) expectedLoss += losses[i] * probabilities[i];
    return obj({
        {"positiveLossProbability", num(probabilities[1] + probabilities[2])},
        {"expectedLoss", num(expectedLoss)},
    });
}

int main() {
    writeJson(std::cout, lesson056(), "");
    std::cout << '\n';
}

// Fintech Math Bootcamp · Lesson 056 of 120
// Discrete and Continuous Random Variables
// Module 06: Probability and Random Variables
//
// Scenario: Distinguishing uncertain counts from uncertain amounts
// Rule:     a random variable maps outcomes to numbers
//
// Try it:   Must an expected value be one of the possible individual outcomes?
//
// Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/discrete-and-continuous-random-variables/
// Free course:    https://courses.thefintechbuilder.com
// Synthetic teaching example, not financial advice or a production library.

// --- Minimal JSON value and printer: objects keep insertion order, 2-space indent. ---

#[allow(dead_code)]
enum Json {
    Null,
    Num(f64),
    Str(String),
    Arr(Vec<Json>),
    Obj(Vec<(String, Json)>),
}

#[allow(dead_code)]
fn nums(values: &[f64]) -> Json {
    Json::Arr(values.iter().map(|&v| Json::Num(v)).collect())
}

#[allow(dead_code)]
fn obj(fields: Vec<(&str, Json)>) -> Json {
    Json::Obj(fields.into_iter().map(|(k, v)| (k.to_string(), v)).collect())
}

fn format_number(v: f64) -> String {
    if !v.is_finite() {
        return "null".to_string();
    }
    if v.fract() == 0.0 && v.abs() < 1e15 {
        return format!("{}", v as i64);
    }
    format!("{:?}", v) // shortest round-trip form
}

impl Json {
    fn render(&self, indent: &str) -> String {
        let inner = format!("{}  ", indent);
        match self {
            Json::Null => "null".to_string(),
            Json::Num(v) => format_number(*v),
            Json::Str(s) => format!("\"{}\"", s),
            Json::Arr(items) if items.is_empty() => "[]".to_string(),
            Json::Obj(fields) if fields.is_empty() => "{}".to_string(),
            Json::Arr(items) => {
                let lines: Vec<String> = items.iter().map(|v| format!("{}{}", inner, v.render(&inner))).collect();
                format!("[\n{}\n{}]", lines.join(",\n"), indent)
            }
            Json::Obj(fields) => {
                let lines: Vec<String> = fields
                    .iter()
                    .map(|(k, v)| format!("{}\"{}\": {}", inner, k, v.render(&inner)))
                    .collect();
                format!("{{\n{}\n{}}}", lines.join(",\n"), indent)
            }
        }
    }
}

// --- Lesson ---

fn lesson056() -> Json {
    let losses: [f64; 3] = [0.0, 100.0, 500.0];
    let probabilities: [f64; 3] = [0.90, 0.08, 0.02];
    let expected_loss: f64 = losses.iter().zip(probabilities.iter()).map(|(l, p)| l * p).sum();
    obj(vec![
        ("positiveLossProbability", Json::Num(probabilities[1] + probabilities[2])),
        ("expectedLoss", Json::Num(expected_loss)),
    ])
}

fn main() {
    println!("{}", lesson056().render(""));
}

/**
 * Fintech Math Bootcamp · Lesson 056 of 120
 * Discrete and Continuous Random Variables
 * Module 06: Probability and Random Variables
 *
 * Scenario: Distinguishing uncertain counts from uncertain amounts
 * Rule:     a random variable maps outcomes to numbers
 *
 * Try it:   Must an expected value be one of the possible individual outcomes?
 *
 * Lesson article: https://thefintechbuilder.com/financial-mathematics-statistics-and-data-foundations/probability-and-random-variables/discrete-and-continuous-random-variables/
 * Free course:    https://courses.thefintechbuilder.com
 * Synthetic teaching example, not financial advice or a production library.
 */

using System;
using System.Linq;
using System.Text.Json;

var options = new JsonSerializerOptions { WriteIndented = true };
Console.WriteLine(JsonSerializer.Serialize(Lesson056(), options));

static object Lesson056()
{
    double[] losses = { 0, 100, 500 };
    double[] probabilities = { 0.90, 0.08, 0.02 };
    return new
    {
        positiveLossProbability = probabilities[1] + probabilities[2],
        expectedLoss = losses.Select((loss, i) => loss * probabilities[i]).Sum(),
    };
}