11. Assume X is a continuous random variable with moment generatng function M(t) -4t+30t2 exp (-4t + 30t), -0

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Q: -, P(T|R) P(RT) 9 Consider two events R and T. Find- 1)P(R' UT) = ? = 3 2/7,P( ,P(ROT) = 116 8

A: From the provided information,

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Q: 4. Let X be a random variable with c.d.f., 0, if x < 0 1 Fx (x) = • if 0sx < 1/2 2' 1, if x 2 1/2…

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A: PGF of a Random Variable is given by, Gx(t) = Σ tx P(X=x)

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Q: If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?

A: is a continuous random variable following a uniform distribution, that is .

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