4.10 Let X be a binomial random variable with parame-tersh and p. Show that:E[(1 - p)*]= (1 - p²n

X be a binomial random variable with parameters n and p. i.e. X ~ bin(n,p)

Answered: 4.10 Let X be a binomial random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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)
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. (a) (X₂) (¹) (X) = (2) 1/√2 (Ⓒ) (x₂) - (3/1² ¹1/1²) (2) (c = 2 0 = 2 Z₁ 1) (²) 3 (4¹) (X) = (²¹) (1) (2) (3) Y₁ 1 (29) - ()) (2) = Y₂ 1 Y₁ (121) = (1/² √₂) (2) (1/√2 1/√2 /2 −1/√√2, Y₂ X₁ X₂ = 22 1 1 2 0 Y₁ 2 1 (4) (2)) = (²) (²) 1 1 Z₁ Z₂ Z3
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Q.2 Find the value of a when Z is a standard normal random variable and P{-3

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4.10 Let X be a binomial random variable with parame- ers h and p. Show that: E[(1 - p)*] = (1 - p²)n