Page 80 - Applied statistics and probability for engineers

58 Chapter 2/Probability

off to the nearest tenth or hundredth of a unit. The random variable that represents this
measurement is said to be a continuous random variable. The range of the random vari-
able includes all values in an interval of real numbers; that is, the range can be thought
of as a continuum.
In other experiments, we might record a count such as the number of transmitted bits that
are received in error. Then, the measurement is limited to integers. Or we might record that
a proportion such as 0.0042 of the 10,000 transmitted bits were received in error. Then, the
measurement is fractional, but it is still limited to discrete points on the real line. Whenever
the measurement is limited to discrete points on the real line, the random variable is said to be
a discrete random variable.

Discrete and
Continuous A discrete random variable is a random variable with a inite (or countably ininite) range.
Random
Variables A continuous random variable is a random variable with an interval (either inite
or ininite) of real numbers for its range.

In some cases, the random variable X is actually discrete but, because the range of possible
values is so large, it might be more convenient to analyze X as a continuous random variable. For
example, suppose that current measurements are read from a digital instrument that displays the
current to the nearest 100th of a milliampere. Because the possible measurements are limited,
the random variable is discrete. However, it might be a more convenient, simple approximation
to assume that the current measurements are values of a continuous random variable.

Examples of
Random Examples of continuous random variables:
Variables
electrical current, length, pressure, temperature, time, voltage, weight
Examples of discrete random variables:
number of scratches on a surface, proportion of defective parts among 1000
tested, number of transmitted bits received in error

Exercises FOR SECTION 2-8

Problem available in WileyPLUS at instructor’s discretion.
Tutoring problem available in WileyPLUS at instructor’s discretion
2-182. Decide whether a discrete or continuous random vari- (c) The number of molecules in a sample of gas.
able is the best model for each of the following variables: (d) The concentration of output from a reactor.
(a) The time until a projectile returns to earth. (e) The current in an electronic circuit.
(b) The number of times a transistor in a computer memory 2-184. Decide whether a discrete or continuous random
changes state in one operation. variable is the best model for each of the following variables:
(c) The volume of gasoline that is lost to evaporation during (a) The time for a computer algorithm to assign an image to a
the illing of a gas tank. category.
(d) The outside diameter of a machined shaft.
(b) The number of bytes used to store a ile in a computer.
2-183. Decide whether a discrete or continuous random (c) The ozone concentration in micrograms per cubic meter.
variable is the best model for each of the following variables:
(a) The number of cracks exceeding one-half inch in 10 miles (d) The ejection fraction (volumetric fraction of blood pumped
of an interstate highway. from a heart ventricle with each beat).
(b) The weight of an injection-molded plastic part. (e) The luid low rate in liters per minute.