. X is the amount of rainfall in Seattle on a randomly chosen day. X is the number of rainy days in Seattle for a randomly chosen week. Practice with a Discrete Distribution . Imagine you are rolling two (six-sided) dice. What are the possibilities you can roll? How can we determine the probability for getting each amount? Make a table representing the probability distribution for the sum X of the amounts shown on the two rolled dice, telling me the story of your thought process for making this table. Use your table to find the following, telling me the story of your thought process for how you do SO: . • P(X=2) P(X> 10) P(X ≤2) . The mean (expected value) of X . The variance and standard deviation of X ● S Suppose we kept one of the usual six-sided dice, but for the other we replaced it with one which has five or six dots on each side instead of the usual one through six. Without actually calculating anything, would the mean increase or decrease? Would the variance and standard deviation increase or decrease? Tell me about your thought process for this. Application to Quality Control - Binomial Distributions

A First Course in Probability (10th Edition)
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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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I'm asking for help with the Practice with a Discrete Distribution problem up to the bullets points, but not the portion that starts with "Suppose..."

X represents whether or not it rains in Seattle on a randomly chosen day.
. X is the amount of rainfall in Seattle on a randomly chosen day.
X is the number of rainy days in Seattle for a randomly chosen week.
Practice with a Discrete Distribution
Imagine you are rolling two (six-sided) dice. What are the possibilities you can roll? How can we determine
the probability for getting each amount? Make a table representing the probability distribution for the sum
X of the amounts shown on the two rolled dice, telling me the story of your thought process for making
this table. Use your table to find the following, telling me the story of your thought process for how you do
SO:
• P(X=2)
P(X> 10)
• P(X ≤2)
. The mean (expected value) of X
.
The variance and standard deviation of X
Suppose we kept one of the usual six-sided dice, but for the other we replaced it with one which has five or
six dots on each side instead of the usual one through six. Without actually calculating anything, would the
mean increase or decrease? Would the variance and standard deviation increase or decrease? Tell me about
your thought process for this.
Application to Quality Control - Binomial Distributions
While working in quality control, your job is to make sure that 95% of the 500 products which leave the
factory each day are up to specifications. To test this, each day you select 25 products at random and check
their quality. If no more than one product is poor quality, it is considered acceptable. If two or more
products are poor quality, you must test all 500 of the products manufactured that day, a costly and time-
M
B
C
US
Transcribed Image Text:X represents whether or not it rains in Seattle on a randomly chosen day. . X is the amount of rainfall in Seattle on a randomly chosen day. X is the number of rainy days in Seattle for a randomly chosen week. Practice with a Discrete Distribution Imagine you are rolling two (six-sided) dice. What are the possibilities you can roll? How can we determine the probability for getting each amount? Make a table representing the probability distribution for the sum X of the amounts shown on the two rolled dice, telling me the story of your thought process for making this table. Use your table to find the following, telling me the story of your thought process for how you do SO: • P(X=2) P(X> 10) • P(X ≤2) . The mean (expected value) of X . The variance and standard deviation of X Suppose we kept one of the usual six-sided dice, but for the other we replaced it with one which has five or six dots on each side instead of the usual one through six. Without actually calculating anything, would the mean increase or decrease? Would the variance and standard deviation increase or decrease? Tell me about your thought process for this. Application to Quality Control - Binomial Distributions While working in quality control, your job is to make sure that 95% of the 500 products which leave the factory each day are up to specifications. To test this, each day you select 25 products at random and check their quality. If no more than one product is poor quality, it is considered acceptable. If two or more products are poor quality, you must test all 500 of the products manufactured that day, a costly and time- M B C US
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