Probabilities and Relative Frequencies Are Related in That the Probability

question 47

Essay

Probabilities and relative frequencies are related in that the probability of an outcome is
the proportion of the time that the outcome occurs in the long run.Hence concepts of
joint, marginal, and conditional probability distributions stem from related concepts of
frequency distributions.
You are interested in investigating the relationship between the age of heads of
households and weekly earnings of households.The accompanying data gives the number
of occurrences grouped by age and income.You collect data from 1,744 individuals and
think of these individuals as a population that you want to describe, rather than a sample
from which you want to infer behavior of a larger population.After sorting the data, you
generate the accompanying table: The median of the income group of $800 and above is $1,050.
(a)Calculate the joint relative frequencies and the marginal relative frequencies.Interpret
one of each of these.Sketch the cumulative income distribution.

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Definitions:

Headwaters

The location or general area where a stream or river begins.

Perennial

Describes plants that live for more than two years or streams that flow continuously throughout the year.

Gradient

A rate of inclination or slope, or the rate at which a physical quantity changes with respect to change in another quantity.

Cross-sectional Area

The area of a particular section of an object or material that is exposed when it is cut through by a plane.