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Let (Xn)neN and (Yn)neN be two sequences of random variables and X and Y some random variables. Which of the following implications are correct: Select one or more: ✓Xn → X in probability and Yn → Y P-a.s. then X₂ + Yn → X + Y in probability. ✔ Xn → X in square mean and Yɲ → Y P-a.s. then Xn + Yn → X + Y in probability Xn → X P-a.s and Yn → Y in probability then Xn + Yn → X + Y P-a.s. Xn → X in probability and Yn → Y in probability then Xn + Yn → X + Y in probability.✔ XnX P-a.s and Yn → Y P-a.s. then Xn + Yn → X + Y in mean square. Xn → X in mean and Yn → Y P-a.s. then X₂ + Yn → X+Y P-a.s.

Let (Xn)neN and (Yn)neN be two sequences of random variables and X and Y some random variables. Which of the following implications are correct: Select one or more: ✓Xn → X in probability and Yn → Y P-a.s. then X₂ + Yn → X + Y in probability. ✔ Xn → X in square mean and Yɲ → Y P-a.s. then Xn + Yn → X + Y in probability Xn → X P-a.s and Yn → Y in probability then Xn + Yn → X + Y P-a.s. Xn → X in probability and Yn → Y in probability then Xn + Yn → X + Y in probability.✔ XnX P-a.s and Yn → Y P-a.s. then Xn + Yn → X + Y in mean square. Xn → X in mean and Yn → Y P-a.s. then X₂ + Yn → X+Y P-a.s.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 35E
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Let (Xn)neN and (Yn)neN be two sequences of random variables and X and Y some random variables. Which of the following implications are correct: Select one or more: ✔ Xn → X in probability and Yn → Y P-a.s. then Xn + Yn → X + Y in probability. Xn → X in square mean and Yn → Y P-a.s. then Xn + Yn → X + Y in probability Xn → X P-a.s and Yn → Y in probability then Xn + Yn → X + Y P-a.s. ✔ Xn → X in probability and Yn → Y in probability then Xn + Yn → X + Y in probability. Xn → X P-a.s and Yn → Y P-a.s. then Xn + Yn → X + Y in mean square. O Xn → X in mean and Yn → Y P-a.s. then Xn+ Yn → X+Y P-a.s.
Transcribed Image Text:Let (Xn)neN and (Yn)neN be two sequences of random variables and X and Y some random variables. Which of the following implications are correct: Select one or more: ✔ Xn → X in probability and Yn → Y P-a.s. then Xn + Yn → X + Y in probability. Xn → X in square mean and Yn → Y P-a.s. then Xn + Yn → X + Y in probability Xn → X P-a.s and Yn → Y in probability then Xn + Yn → X + Y P-a.s. ✔ Xn → X in probability and Yn → Y in probability then Xn + Yn → X + Y in probability. Xn → X P-a.s and Yn → Y P-a.s. then Xn + Yn → X + Y in mean square. O Xn → X in mean and Yn → Y P-a.s. then Xn+ Yn → X+Y P-a.s.
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