D. Assume that X1, X2, ...,X, is a random sample from a r(1,0) distribution1. The moment generating function of the random variable E-1 Xị is given byi%3D1M22(t) = (1 – 2t)- 9.2. The random variable E-1 x; has a X2-distribution with 9 degrees of freedom.3. The (1-a)100% confidence interval of 0 is given by218'1-플18

Answered: D. Assume that X1,X2, ... ,X, is a…

A First Course in Probability (10th Edition)

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1. A discrete random variable X follows the Uniform distribution if X takes values x = 1, 2, .., N, with P(X = x) = 1/N. Compute E(X), E(X²) and the variance Var(X). You may use the following identities: п(п + 1) (1) 2 п(п + 1)(2n + 1) (2) i=1
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Q 6.1. Suppose Z = (Z₁, Z2, Z3) is a standard multi-variate Gaussian random variable i.e., for i ≤ 3, Zi~ N(0, 1) are i.i.d. random variables. Each of the random variables, (a)–(d), on the left is equal in distribution to exactly one random variables, (1)–(4), on the right. Pair up according to "equal in distribution" and explain briefly your reasoning. X₁ (a) X₂ (b) (x₂) - (2) (c) (x²) - (¹/1² 1/√²) (2₁) (3/√2 = √2 = (V2) Z₁ (d) (x) - (1) (²) X2 Y₁ (9)-(-) (2) (1=1) Y₂ (1) Y₁ (²) (4) - (1/² (3) (1/√√2 1/√2-1/√2) (x₁) = (²₁ ² ✓/³²) (3) 2 2 √2 1 Z3 Y₁ → ()-()) (4) = Y₂ 1/2) (2) 1) (2)
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D. Assume that X1,X2, ... ,X, is a random sample from a r(1,0) distribution 1. The moment generating function of the random variable E-1 xi is given by Mar (t) = (1 – 2t)- 9. 2. The random variable E-1 x; has a X2-distribution with 9 degrees of freedom. i=D1