An item (say, a pen) from a production line can be acceptable, repairable or useless. Suppose a production is stable and let p, q, r (p + q + r = 1), denote the probabilities for three possible conditions of an item. If the items are put into lots of 100: (i) Derive an expression for the probability function of (X,Y), where X and Y are the number of items in the lots that are respectively in the first two conditions. (ii) Derive the moments generating functions of X and Y. (iii) Find the marginal distribution 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.
An item (say, a pen) from a production line can be acceptable, repairable
or useless. Suppose a production is stable and let p, q, r (p + q + r = 1),
denote the probabilities for three possible conditions of an item. If the items
are put into lots of 100:
(i) Derive an expression for the probability function of (X,Y), where X
and Y are the number of items in the lots that are respectively in the first
two conditions.
(ii) Derive the moments generating
(iii) Find the marginal distribution of X.
(iv) Find the conditional distribution of Y given X=90.
(v) Obtain the regression function of Y on X.
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