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Calculo de probabilidades usando la f.d.p. de una V.A. continua, ejemplo 4
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Calculo de probabilidades usando la f.d.p. de una V.A. continua, ejemplo 4

Calculating Probability Using Density Functions

Introduction to Probability Calculation

  • The discussion begins with the intent to calculate the probability of a variable x being between 1 and 3 using a density function.
  • The integral of the density function over the interval from 1 to 3 represents an area under the curve, which corresponds to this probability.

Understanding Density Functions

  • The speaker emphasizes that calculating this probability involves finding the area under the density function's curve between specified limits (1 and 3).
  • The density function is defined piecewise: for x from 0 to 2, it is 1/4x , and for x greater than 2, it becomes 1 - 1/4x .

Performing Integrals

  • To find probabilities, integrals are computed separately for each segment of the piecewise function. For example, from 1 to 2, we integrate 1/4x .
  • The calculations involve evaluating integrals such as int_1^2 x^2/2 dx + ..., leading to specific numerical results.

Final Calculations and Results

  • After performing all necessary evaluations and simplifications, results are consolidated into fractions with common denominators for easier computation.
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 esteé entre 1 y 3. Playlist variable aleatoria continua: https://www.youtube.com/playlist?list=PLubBiyKUarkeSR_cccALGUN7o8faookzb https://www.instagram.com/p/B8sXPufnDk_/?utm_source=ig_web_copy_link