Let X be a random variable having a cumulative distribution function F. Show that if EX exists, then | (1- F(x))dx – | F(x)dx. EX By Fubini's theorem,

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A: Here, we have to prove EY=∫-∞∞yfydy.

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: (i) As if f(x) is a pdf then ∫-∞∞f(x)dx = 1⇒ ∫01axdx + ∫12adx + ∫23(-ax + 3a)dx = 1⇒ ax2201 + ax12 +…

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A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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A: Since you have posted multiple questions, I have answered only one f(x)=kx     for x=2,3,40,…

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Q: :Let X be a continuous random variable with distribution Kif f(x)= { 0≤x≤8 elsewhere 1. Find P (2 ≤…

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A: Hello! As you have posted 2 different questions, we are answering the first question (2.2.5). In…

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A: Given that                      We have to find  Var(X)  And  P(1/2&lt;X&lt;1, 0&lt;Y&lt;1/2)

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Q: a. If X is a Poisson variate such that 2P(X=0)=P(X=2),find the probability that P(XS3).

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A: Cumulative Distribution Function is the probability that shows the overall chance of occurrence of…