Suppose you conduct a series of experiments, each of which consists of tossing a fair coin 6 times. Let X be the number of heads. In each of the following questions, give your reasoning. - What are the probabilities of each value of X? - What is P(the first toss is tails | X=3)? - What is P(X = 3 | given the first toss is tails)? - What is P(the first experiment where X=5 is the eighth)? What is P( X < 5)? - What are the mean and variance of X?
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.
Q 2(a)
Suppose you conduct a series of experiments, each of which consists of tossing a fair coin 6 times. Let X be the number of heads.
In each of the following questions, give your reasoning.
- What are the probabilities of each value of X?
- What is P(the first toss is tails | X=3)?
- What is P(X = 3 | given the first toss is tails)?
- What is P(the first experiment where X=5 is the eighth)? What is P( X < 5)?
- What are the mean and variance of X?
2.b.
Suppose one evening 6 people meet in a restaurant for dinner. They have spent the previous day apart from each other. Then later that night all 6 fall ill with food poisoning. What do you think is the most probable explanation? Explain your answer using Bayes Theorem.
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