You have a bag of 1 gold coin, 2 red coins and 3 blue coins and you can only select two at random to keep. a) What is the probability of picking two coins of the same color? Let G be the random variable counting the number of gold coins kept , R being the random variable counting the number of red coins kept and B being the random variable counting the number of blue coins kept. b) i) Determine the joint probability mass function of the random variables G and R and express in a table. (Also how do you check this?) ii) What is the name of the distribution of G, define the parameters. [Data table was requested however none was given with this question as the probability of picking certain color of coin from the bag is only dependant on the number of coins for each color, so if their were only one coin for each color in the bag so that S = {gold,red,blue} and you had to randomly pick one, the probability of picking any color would be 1/3]
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
You have a bag of 1 gold coin, 2 red coins and 3 blue coins and you can only select two at random to keep.
a) What is the probability of picking two coins of the same color?
Let G be the random variable counting the number of gold coins kept , R being the random variable counting the number of red coins kept and B being the random variable counting the number of blue coins kept.
b) i) Determine the joint probability mass
ii) What is the name of the distribution of G, define the parameters.
[Data table was requested however none was given with this question as the probability of picking certain color of coin from the bag is only dependant on the number of coins for each color, so if their were only one coin for each color in the bag so that S = {gold,red,blue} and you had to randomly pick one, the probability of picking any color would be 1/3]
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