Consider the following contingency table : What is the probability of a . A | B ? b . A ' | B ' ? c . A | B ' ? d. Are event A and B independent?
Consider the following contingency table : What is the probability of a . A | B ? b . A ' | B ' ? c . A | B ' ? d. Are event A and B independent?
Solution Summary: The author determines the probability of the event ‘ A|B’. According to the provided information, a contingency table is given for the events A and B.
Definition Definition Visual representation of the relationship between two or more categorical variables. A contingency table is a categorical version of the scatterplot, which is used to visualize the linear relationship between two variables.
A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected.
a) Calculate the percentage of components that get rejected.
b) In a manufacturing run of 1000 units, how many are expected to be rejected?
c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.
5. Let X and Y be independent random variables and let the superscripts denote
symmetrization (recall Sect. 3.6). Show that
(X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose
that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
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