A class of n students takes a test consisting of m questions. Suppose that student i submitted answers to the first m_i, for m_i <= m questions. The grader randomly picks one answer, call it (I, J) where I is the student ID number (values 1,...,n) and J is the question number (values 1,...,m). Assume that all answers are equally likely to be picked. Calculate the joint and marginal PMFs of I and J. Assume that an answer to question j if submitted by student i is correct with probability p_ij. Each answer gets a points if it is correct and b points otherwise. Find the expected value of the score of student i.
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.
- A class of n students takes a test consisting of m questions. Suppose that student i submitted answers to the first m_i, for m_i <= m questions.
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The grader randomly picks one answer, call it (I, J) where I is the student ID number (values 1,...,n) and J is the question number (values 1,...,m). Assume that all answers are equally likely to be picked. Calculate the joint and marginal PMFs of I and J.
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Assume that an answer to question j if submitted by student i is correct with
probability p_ij. Each answer gets a points if it is correct and b points otherwise. Find theexpected value of the score of student i.
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