Problem 1. An egg was put in a pot filled with hot water, in order to warm it. Suppose that at the initial moment the egg temperature was T, , and the water temperature in the pot was 0, ; suppose also that the ambient air has the temperature Tm. Assume that the heat capacity of the pot is much larger than that of the egg, so that we can neglect the influence of the egg on the water temperature in the pot. Then the temperatures and of the egg and of the water in the pot are described by the equations: k(T – 0), dt = km (0 – Tm) , where k, km < 0. dt (a) Find the egg temperature T(t) and the pot temperature 0 (t) for distinct constants k and km. (b) The same, for k = km: (c) Find lim T(t) and lim 0(t) in both cases above.

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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.