Homework Help is Here – Start Your Trial Now!
Math
Probability
Suppose X₁, X2, and X3 are independent random variables where X₁~ N(μ₁ = 1,0²= 1²) X₂~ N(₂=2,0²2 =2²) X3 ~ N(μ3 = 3,0² = 3²) (a) Let W = X₁ X2. What is the distribution of W? Be sure to state all parameters. Show your work using clear notation

Suppose X₁, X2, and X3 are independent random variables where X₁~ N(μ₁ = 1,0²= 1²) X₂~ N(₂=2,0²2 =2²) X3 ~ N(μ3 = 3,0² = 3²) (a) Let W = X₁ X2. What is the distribution of W? Be sure to state all parameters. Show your work using clear notation

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
See similar textbooks
icon
Related questions
Question

hi, I would like to help with these question.

Thank you.

1. Suppose X₁, X2, and X3 are independent random variables where = X₁~ N(μ₁ 1,0² = 1²) X₂ ~ N(₂=2,02 = 2²) X3 ~ N(μ3 = 3,0²3 = 3²) (a) Let W = X₁ X2. What is the distribution of W? Be sure to state all parameters. Show your work using clear notation. (b) Using your answer in (la), find P(X₁ > X₂). Show your work using clear notation. (c) Let W = X₁ - 6X2+2X3. What is the distribution of W? Be sure to state all parameters. Show your work using clear notation. (d) Using your answer in (1c), find P(X₁ − 6X2 > 5 – 2X3). Show your work using clear notation. 2. An artist makes pottery. There are two major steps: wheel throwing and firing. The time (in minutes) for wheel throwing can be modeled by a X₁~ N(μ = 40, o² = 22) distribution and the time for firing can be modeled by a X₂ ~ N(μ = 60,0² = 32) distribution. Assume independence. (a) Determine the probability that a piece of pottery will be completed in less than 95 minutes. (b) Determine the probability that a piece of pottery will take longer than 110 minutes. (c) Determine the probability that 2X₁ > 1.5X₂. (d) Determine the probability that 2X₁ > X₂ + 15. (e) Suppose 10 pieces of pottery are randomly selected. Determine the probability that the mean firing time X is between 58 and 61 minutes. (f) Suppose 10 pieces of pottery are randomly selected. Let X denote the sample mean firing time. Determine the 10th percentile of X. (g) Determine the probability that 2 pieces of pottery will take less than 210 minutes using a linear combination. Think carefully when doing this problem. Note that we can not simply find P(2X₁ +2X₂ < 210). Hint: Let Y₁ denote the completion time for the first piece, and let Y₂ denote the completion time for the second piece. 3. Suppose X₁, X2, and X3 are independent random variables where X₁ ~ N(μ₁ = μ₁0 = 1²) X₂ ~ N(μ₂ = μ,0²2 =2²) X3 ~ N(μ3μ,03 = 3²) = If 0.9 = P(5X₁ + 2X2 − 4X3 > 10), find μ.
Transcribed Image Text:1. Suppose X₁, X2, and X3 are independent random variables where = X₁~ N(μ₁ 1,0² = 1²) X₂ ~ N(₂=2,02 = 2²) X3 ~ N(μ3 = 3,0²3 = 3²) (a) Let W = X₁ X2. What is the distribution of W? Be sure to state all parameters. Show your work using clear notation. (b) Using your answer in (la), find P(X₁ > X₂). Show your work using clear notation. (c) Let W = X₁ - 6X2+2X3. What is the distribution of W? Be sure to state all parameters. Show your work using clear notation. (d) Using your answer in (1c), find P(X₁ − 6X2 > 5 – 2X3). Show your work using clear notation. 2. An artist makes pottery. There are two major steps: wheel throwing and firing. The time (in minutes) for wheel throwing can be modeled by a X₁~ N(μ = 40, o² = 22) distribution and the time for firing can be modeled by a X₂ ~ N(μ = 60,0² = 32) distribution. Assume independence. (a) Determine the probability that a piece of pottery will be completed in less than 95 minutes. (b) Determine the probability that a piece of pottery will take longer than 110 minutes. (c) Determine the probability that 2X₁ > 1.5X₂. (d) Determine the probability that 2X₁ > X₂ + 15. (e) Suppose 10 pieces of pottery are randomly selected. Determine the probability that the mean firing time X is between 58 and 61 minutes. (f) Suppose 10 pieces of pottery are randomly selected. Let X denote the sample mean firing time. Determine the 10th percentile of X. (g) Determine the probability that 2 pieces of pottery will take less than 210 minutes using a linear combination. Think carefully when doing this problem. Note that we can not simply find P(2X₁ +2X₂ < 210). Hint: Let Y₁ denote the completion time for the first piece, and let Y₂ denote the completion time for the second piece. 3. Suppose X₁, X2, and X3 are independent random variables where X₁ ~ N(μ₁ = μ₁0 = 1²) X₂ ~ N(μ₂ = μ,0²2 =2²) X3 ~ N(μ3μ,03 = 3²) = If 0.9 = P(5X₁ + 2X2 − 4X3 > 10), find μ.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 10 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Calculus For The Life Sciences
Calculus For The Life Sciences
Calculus
ISBN:
9780321964038
Author:
GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:
Pearson Addison Wesley,
SEE MORE TEXTBOOKS