Statistics Assignment, USM, Malaysia Let X be an exponential random variable, Show that for a > 0 and b > 0

University Universiti Sains Malaysia (USM)
Subject Statistics

Question

  • Let X be an exponential random variable, Show that for a > 0 and b > 0,

P(X >a+b|X> a) = PX > b)

  • Let ¥ be a continuous random variable with a density function given as follows,

Statistics

  • Identify the distribution function for Y and state the parameters of the distributions.
  • Derive the moment-generating function of Y,
  • Given the E(Y`) = 15, find the value of 62.
  • Use the information in (iii) to find the value of 0025 if P(Y > 00,25) = 0.75,

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