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

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,

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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