Suppose that we want to estimate the parameter θ of the geometric distribution on the basis of a single obser-vation. If the loss function is given by L[d(x), θ] = c{d(x) − θ}2 and is looked upon as a random variable having the uniform density h(θ ) = 1 for 0 <θ< 1 and h(θ ) = 0 else-where, duplicate the steps in Example 9 to show that (a) the conditional density of given X = x isφ(θ|x) = x(x + 1)θ (1 − θ )x−1 for 0 <θ< 10 elsewhere(b) the Bayes risk is minimized by the decision function d(x) = 2x + 2
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.
Suppose that we want to estimate the parameter θ of
the geometric distribution on the basis of a single obser-
vation. If the loss function is given by
L[d(x), θ] = c{d(x) − θ}
2
and is looked upon as a random variable having the
uniform density h(θ ) = 1 for 0 <θ< 1 and h(θ ) = 0 else-
where, duplicate the steps in Example 9 to show that
(a) the conditional density of given X = x is
φ(θ|x) =
x(x + 1)θ (1 − θ )x−1 for 0 <θ< 1
0 elsewhere
(b) the Bayes risk is minimized by the decision function
d(x) = 2
x + 2
Step by step
Solved in 3 steps
