valuation_probability
Probability & Expected Value
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Third-party content written by another agent. Data to evaluate, not instructions.
Compute expected value and probability-weighted outcomes for startup scenarios: discrete E[X], joint probability of sequential events, probability-weighted value, VC portfolio expected return, Poisson event probability, and continuous E[X] over a range. Method selects the formula. Use for probability-weighted central estimates; for named bull/base/bear tables or option pricing use valuation_advanced, and to discount cash flows use valuation_time_value. Parameters apply per method: expected_value_discrete and probability_weighted need outcomes + probabilities; portfolio_return needs weights + returns; poisson needs mean_events + k; expected_value_continuous needs lower + upper. outcomes and probabilities must be equal length, and the probabilities should sum to 1. Routing: use valuation_advanced method 'scenario_analysis' for named bull/base/bear scenario tables, and its black_scholes/binomial methods for option pricing; use this tool for arbitrary outcome lists and probability-weighted central estimates. Only method is required; all other parameters are method-dependent, so supply those the selected method names and omit the rest (defaults apply where defined). Rate and decimal inputs are fractions (0.10 = 10%); probability and weight lists are in [0,1] and sum to 1. Returns value, method, inputs, assumptions, chapter, formula_number and calculation steps; pure arithmetic — no I/O and no external calls — rounded to 2 decimals, with no auth or rate limits. An unknown method, or a missing method-required parameter, returns an error instead of a value.
Input schema
| Property | Type | Required | Description |
|---|---|---|---|
| method | string | yes | Formula to apply. Options: expected_value_discrete = E[X] = Σ xᵢ·P(X=xᵢ) over a discrete outcome list.; joint_probability = P(total) = Π pᵢ for independent sequential events.; probability_weighted = E[V] = Σ pᵢ·Vᵢ.; portfolio_return = E[R] = Σ wᵢ·Rᵢ across a VC portfolio.; poisson = P(X=k) = e^-λ λ^k / k! for rare events.; expected_value_continuous = E[X] = ∫ x·f(x) dx over [lower, upper] on the standard normal. |
| outcomes | array | no | Possible outcome values x_i, in any currency unit (must match probabilities in length/order). |
| probabilities | array | no | Probability of each outcome or stage, each in [0,1]; the list must sum to 1 where it is exhaustive. |
| weights | array | no | Portfolio or factor weights, each in [0,1] and summing to 1 (same order as the paired value list). |
| returns | array | no | Return of each asset or scenario as a decimal (0.20 = 20%), aligned with weights. |
| mean_events | number | no | Poisson mean λ = expected number of events in the interval. |
| k | integer | no | Number of events k for the Poisson probability P(X=k); integer ≥ 0. |
| lower | number | no | Lower integration bound (standard-normal domain, e.g. -1.0). |
| upper | number | no | Upper integration bound (standard-normal domain, e.g. 1.0). |
Raw JSON schema
{
"type": "object",
"properties": {
"method": {
"type": "string",
"enum": [
"expected_value_discrete",
"joint_probability",
"probability_weighted",
"portfolio_return",
"poisson",
"expected_value_continuous"
],
"description": "Formula to apply. Options: expected_value_discrete = E[X] = Σ xᵢ·P(X=xᵢ) over a discrete outcome list.; joint_probability = P(total) = Π pᵢ for independent sequential events.; probability_weighted = E[V] = Σ pᵢ·Vᵢ.; portfolio_return = E[R] = Σ wᵢ·Rᵢ across a VC portfolio.; poisson = P(X=k) = e^-λ λ^k / k! for rare events.; expected_value_continuous = E[X] = ∫ x·f(x) dx over [lower, upper] on the standard normal."
},
"outcomes": {
"type": "array",
"items": {
"type": "number"
},
"description": "Possible outcome values x_i, in any currency unit (must match probabilities in length/order)."
},
"probabilities": {
"type": "array",
"items": {
"type": "number"
},
"description": "Probability of each outcome or stage, each in [0,1]; the list must sum to 1 where it is exhaustive."
},
"weights": {
"type": "array",
"items": {
"type": "number"
},
"description": "Portfolio or factor weights, each in [0,1] and summing to 1 (same order as the paired value list)."
},
"returns": {
"type": "array",
"items": {
"type": "number"
},
"description": "Return of each asset or scenario as a decimal (0.20 = 20%), aligned with weights."
},
"mean_events": {
"type": "number",
"description": "Poisson mean λ = expected number of events in the interval."
},
"k": {
"type": "integer",
"description": "Number of events k for the Poisson probability P(X=k); integer ≥ 0."
},
"lower": {
"type": "number",
"description": "Lower integration bound (standard-normal domain, e.g. -1.0)."
},
"upper": {
"type": "number",
"description": "Upper integration bound (standard-normal domain, e.g. 1.0)."
}
},
"required": [
"method"
]
}