Create an R program. Use simulations to prove that the binomial distribution is correct. Recall that the binomial distribution has two parameters n and p. There are n trials and each has two possible outcomes, with probability p for “success” and 1-p for “failure”. The binomial gives the probability distribution for the number of successes in n trials. You will conduct simulations with r replicates, where each simulation replicates does n simulated “coin flips”. You will add up the number of successes in each coin flip, and compare the result to the true distribution: Generate n*r values from the uniform(0,1) distribution and arrange these in an rxn matrix. Each value less than p is considered a “success” For each row from part I, count the number of successes. The number of possible successes ranges from 0 to n Use the table function in R to count up the number of replicates with each number of successes. Make a table that compares the simulation result to the true binomial probabilities. **make calculations as "vectorized" as possible. No use of loops
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.
Create an R program. Use simulations to prove that the binomial distribution is correct. Recall that the binomial distribution has two parameters n and p. There are n trials and each has two possible outcomes, with probability p for “success” and 1-p for “failure”. The binomial gives the probability distribution for the number of successes in n trials. You will conduct simulations with r replicates, where each simulation replicates does n simulated “coin flips”. You will add up the number of successes in each coin flip, and compare the result to the true distribution:
- Generate n*r values from the uniform(0,1) distribution and arrange these in an rxn matrix. Each value less than p is considered a “success”
- For each row from part I, count the number of successes. The number of possible successes ranges from 0 to n
- Use the table function in R to count up the number of replicates with each number of successes.
- Make a table that compares the simulation result to the true binomial
probabilities.
**make calculations as "vectorized" as possible. No use of loops
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