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Calculo de probabilidades usando la f.d.p. de una V.A. continua, ejemplo 2
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Calculo de probabilidades usando la f.d.p. de una V.A. continua, ejemplo 2

Understanding Probability Density Functions

Introduction to Probability Density Function (PDF)

  • The video introduces a probability density function (PDF) defined in two segments: 1/4x for x between 0 and 2, and 1 - 1/4x for x between 2 and 4. Outside these intervals, the PDF is zero.

Calculating Probabilities

  • To calculate probabilities for continuous variables, integration is necessary. The speaker emphasizes that since x varies over real intervals, we must integrate the PDF.

Example of Integration

  • To find the probability that x < 1/2 , we set up an integral from negative infinity to 1/2 . This integral represents the cumulative distribution function (CDF).
  • Since the PDF is zero from negative infinity to zero, we can simplify our calculation by integrating from zero to 1/2 .

Evaluating the Integral

  • The integral of the PDF from 0 to 1/2 , which is represented as int_0^1/2 (1/4x),dx, needs evaluation.

Result of Integration

  • Upon evaluating this integral, it results in a value expressed as a fraction involving squares and constants.
  • Specifically, substituting values into the evaluated expression yields a final result of P(x < 1/2) = 1/32.

Interpretation of Results

Playlists: Probabilida de variables aleatorias continuas
Video description

En este video usamos la función de densidad de probabilidad de una variable aleatoria continua X para encontrar Probabilidad de que x sea menor a 1/2 . Playlist variable aleatoria continua: https://www.youtube.com/playlist?list=PLubBiyKUarkeSR_cccALGUN7o8faookzb https://www.instagram.com/p/B8sXPufnDk_/?utm_source=ig_web_copy_link