Download For the following exercise determine the range (possible values) of

BH#4 Problems 3-6, 3-10
ENGR 323
HOPPER
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For the following exercise determine the range (possible values) of
the random variable.
Problem 3-6
The random variable is the moisture content of a lot of
raw material measured to the nearest percentage point.
Background:
A random variable, as defined on p.100, is a function
that assigns a real number to each outcome in the sample
space of a random experiment. It’s notation is denoted
by an uppercase letter such as X.
Here the random variable is defined as: X = percent moisture content of a
lot of raw material
The range of the random variable is the set of all possible numbers
which can be assigned to the random variable. The notation associated with
the range is the lower case letter corresponding to the random variable.
Here it would be x.
Solution: The range of X, for Problem 3-6 is stated to be all possible
real number percentage points.
In this case, we could model the percent moisture content as a
discrete random variable, or as a continuous random variable. A discrete
random variable is a random variable with a finite or countably infinite
range. (see p.102 for the definition.) For example, in this problem the
discrete range would be:
x = {0,1,2,3,...,100}
In contrast, a continuous random variable can take on an infinitely
countable number of values. In this case, the range of X would include all
fractional elements as well as whole numbers. For example, in this
problem the continuous range would be:
x= {0,0.1,0.11,...,1,...,2,...,3,...,100}
This set is much larger than the first because it includes all possible real
values between the whole numbers.