1. Suppose that the number of red blood corpuscles in humans, denoted by X, follows a Poisson distribution whose parameter depends on the observed individual. For a person selected at random we may consider the parameter value Y as an that Y y, we have X Exp(a) random variable such that, given Poisson(y); namely, Exp(a) X | Y yPoisson(y), with Y Here a is a positive constant and the density function of Exp(a) is f(y)aeay, y > 0 (a) Find the conditional expectation E(X|Y = y), where y 0 (b) Compute the expectation E(X). Remark: You may use the law of total expectation. (c) Find the distribution of X. Remark: You may use the law of total probability: P(X k) = So P(X k|Y y)fy (y)dy
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.
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