How to check if a PDF satisfies the requirement for being a density function скачать в хорошем качестве

How to check if a PDF satisfies the requirement for being a density function

#probability A probability density function (PDF) must satisfy two essential conditions to be considered valid: 1. Non-Negativity Condition The function must never take negative values across its entire domain. Since probability cannot be negative, every output of the function should be zero or greater. To verify this: Examine the function to ensure it is always non-negative. Identify any regions where the function may dip below zero. If such regions exist, the function is not a valid PDF. 2. Total Probability Must Be 1 The function must represent a complete probability distribution, meaning the total probability over all possible values must equal 1. This is checked by integrating the function over its entire range: If the total probability is less than 1, the function does not cover all possible outcomes. If the total probability is greater than 1, the function overestimates the probability, which is invalid. If the total probability is exactly 1, the function satisfies this requirement. Verification Process To confirm that a given function is a valid PDF, follow these steps: Check Non-Negativity: Ensure the function does not produce negative values anywhere in its domain. Evaluate the Total Probability: Compute the integral of the function across its entire range. If necessary, adjust the function with a normalization factor to ensure the total probability is exactly 1.#probability