Let Y be a continuous random variable with cumulative distribution function: B A C C D D E √2 In √√2 In ¹ (C) (D) a-2√In2 (E) a +2√In2 -{i- a + F(y) = where a is a constant. What is the 75th percentile of Y? (A) F(0.75) (B) a- 1-e-(y-a)², for y sa otherwise

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A: The solution is given below.Explanation:Given:Given the probability density function (pdf) for a…

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A: Given: The probability generating function of a random variable X is given as:…

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A: Solution: We need to find the value of constant a and the marginal probabilities for X and Y

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Q: Exercise 3. Let X be a random variable with mean µ and variance o². For a E R, consider the…

A: Farmula used  V(X)=E(X2)-[E(X)]2

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Q: [Q1] The probability distribution of the discrete random variable X is: f(X) = k23-x , for x =…

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A: The moment generating function is defined as MX(t) = E(etx)

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A: Suppose X follows an exponential distribution with parameter λ. The RHS is given by:

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Q: - Find the cumulative distribution. Find P(x41. 5

A: The cumulative distribution fu⁸nction of X is defined as F(x) = P(X ≤ x)

Q: (b)A random variable is defined as 172⁄(3X+1); X = 0 ,1,2,3,4,5,6. Construct the PDF of X, and…

A: Question: A random variable is defined as 172⁄(3X+1); X = 0 ,1,2,3,4,5,6. Construct the PDF of X,…

Q: B) Let the random variable X have the moment generating function e3t M(t) 1- t? for -1<t < 1, What…

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Q: (a) Are X and Y statistically independent

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Q: (b)Let X be a random variable with p.d.f. fx) c *123 zero elsewhere. Find the constant c.

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Q: 2. Let X be a random variable with pdf fx(x), and Y = X². %3D (a) Find fx(x|X > 0) (b) Find fy(y|X >…

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A: Method: integration of continuous distribution.The pdf of continuous random variable  is:

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Q: eX with PDF oth

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