A probability mass function for a particular random variable y having nonnegative integer values is defined by the relation P(Y= y)=P(Y=y-1), y=1,2,... Produce the probability mass function of Y. Obtain the moment generating function of Y. Hence, derive the moment generating function of W=3-4Y. ||||||||||||||||||||||||||||||||||

Q: Let X - Unif(0, 2) and Y - Unif(0, 1). Find the probability P(X > Y) that X is greater than Y

A: # Here  given that X~U nia,b       fx =1b-a   '   a≤x≤b  0            ' other

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A: P(a<X<b) = F(b) - F(a) F(a) + P(a<X<b) = F(b)

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A: Solution

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A: Here, we have

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A: Given information: It is given that X be a finite random variable on the sample space.

Q: P(-∞ < x≤ a₁₂) = P(a₁ ≤ x ≤ a₂) = P(a₂ ≤ x ≤ a3) = P(a3 ≤ x < ∞) = function p(x) a₁ = = 1 π(1 + x²)…

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A: E(|X-Y|) fx|y=1n2 E(Z) = ∑x=1n∑y=1nx-yn=∑x=1n ∑y=1n x-yn2+∑…

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A: From the given information, the pdf of the random variable X is,

Q: Theorem 3-14. For a fixed B with P( B) > 0, P (A \ B) is probability function.

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