Let X₁ and X₂ be independent r.v.'s having the same distribution, taking on values 0 and 1 with respective probabilities 0.2 and 0.8. Answer Questions 12 and 13 below. Question 12 Write the m.g.f. of X₁ + X₂ +2. ○ (0.2+0.8e²)2%e²z (0.2e + 0.8e²²) e²z 0 (1 +0.²e² ) ² e²z ○ (0.2 +0.8e²) ²e²z Question 13 Write the m.g.f. of X₁ - 2X₂. ○ (0.2 +0.8e²) (0.2+0.8e-²²) ○ (0.8e + 0.2e²) (0.2e + 0.8e-2²) ○ (0.2e + 0.8e²) (0.2e-² +0.8e-²²) ○ (0.2e² +0.8e-²) (0.2e-² +0.8e²)

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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Let X₁ and X₂ be independent r.v.'s having the same distribution, taking on values 0 and 1 with
respective probabilities 0.2 and 0.8. Answer Questions 12 and 13 below.
Question 12
Write the m.g.f. of X₁ + X₂ + 2.
(0.2+0.8e²) ²% e²z
○ (0.2e + 0.8e²x) e²z
(1 + 0.² e² )² e²²
(0.2+0.8e²)² e²z
Question 13
Write the m.g.f. of X₁ – 2X₂.
(0.2 +0.8e²) (0.2 +0.8e-2²)
(0.8e + 0.2e²) (0.2e + 0.8e-2²)
(0.2e +0.8e²) (0.2e-² +0.8e-²²)
O (0.2e² +0.8e-²) (0.2e + 0.8e²)
Transcribed Image Text:Let X₁ and X₂ be independent r.v.'s having the same distribution, taking on values 0 and 1 with respective probabilities 0.2 and 0.8. Answer Questions 12 and 13 below. Question 12 Write the m.g.f. of X₁ + X₂ + 2. (0.2+0.8e²) ²% e²z ○ (0.2e + 0.8e²x) e²z (1 + 0.² e² )² e²² (0.2+0.8e²)² e²z Question 13 Write the m.g.f. of X₁ – 2X₂. (0.2 +0.8e²) (0.2 +0.8e-2²) (0.8e + 0.2e²) (0.2e + 0.8e-2²) (0.2e +0.8e²) (0.2e-² +0.8e-²²) O (0.2e² +0.8e-²) (0.2e + 0.8e²)
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