Chapter 6 Continuous
Probability Distribution |
Study Guide, Practice
Questions & Exam
Review
|Guaranteed success|
, Discrete the random variable assumes a countable number of distinct values.
Continuous the random variable is characterized by (infinitely) uncountable values within any
interval.
Continuous Random Variables and the Uniform When computing probabilities for a continuous random variable, keep in mind
Distribution that P(X=x) = 0.
- We cannot assign a nonzero probability to each infinitely uncountable value and
still have the probabilities sum to one.
- Thus, since P(X= a) and P(X= b) both equal zero, the following holds for
continuous random variables: (refer to the attached image)
For a discrete random variable X, there are a countable number of possible values.
Probability Density Function f(x) of a continuous - Describes the relative likelihood that X assumes a values within a given
random variable X. interval, where:
> f(x) > 0 for all possible values of X.
> The area under f(x) over all values of x equals one.
Cumulative Density Function F(x) of a continuous - For any value x of the random variable X, the cumulative distribution function
random variable X. F(x) is computed as : (refer to the attached image)
Continuous Uniform Distribution - Describes a random variable that has an equally likely chance of assuming a
value within a specified range.
Graph of the continuous uniform distribution: - The values a and b on the horizontal axis represent the lower and upper limits,
respectively.
- The height of the distribution does not directly represent a probability.
- It is the are under f(x) that corresponds to probability.
Which of the following can be represented by a a) The high daily temperature in Tampa, Florida during the month of July,
continuous random variable? measured in degrees.
a) The high daily temperature in Tampa, Florida during
the month of July, measured in degrees.
b) The number of customers who visit a department
store between 10:00 am and 11:00 am on Mondays.
c) The number of typos found on a randomly selected
page of a textbook.
d) The number of students who will get financial
assistance in a group of 50 randomly selected students.
Probability Distribution |
Study Guide, Practice
Questions & Exam
Review
|Guaranteed success|
, Discrete the random variable assumes a countable number of distinct values.
Continuous the random variable is characterized by (infinitely) uncountable values within any
interval.
Continuous Random Variables and the Uniform When computing probabilities for a continuous random variable, keep in mind
Distribution that P(X=x) = 0.
- We cannot assign a nonzero probability to each infinitely uncountable value and
still have the probabilities sum to one.
- Thus, since P(X= a) and P(X= b) both equal zero, the following holds for
continuous random variables: (refer to the attached image)
For a discrete random variable X, there are a countable number of possible values.
Probability Density Function f(x) of a continuous - Describes the relative likelihood that X assumes a values within a given
random variable X. interval, where:
> f(x) > 0 for all possible values of X.
> The area under f(x) over all values of x equals one.
Cumulative Density Function F(x) of a continuous - For any value x of the random variable X, the cumulative distribution function
random variable X. F(x) is computed as : (refer to the attached image)
Continuous Uniform Distribution - Describes a random variable that has an equally likely chance of assuming a
value within a specified range.
Graph of the continuous uniform distribution: - The values a and b on the horizontal axis represent the lower and upper limits,
respectively.
- The height of the distribution does not directly represent a probability.
- It is the are under f(x) that corresponds to probability.
Which of the following can be represented by a a) The high daily temperature in Tampa, Florida during the month of July,
continuous random variable? measured in degrees.
a) The high daily temperature in Tampa, Florida during
the month of July, measured in degrees.
b) The number of customers who visit a department
store between 10:00 am and 11:00 am on Mondays.
c) The number of typos found on a randomly selected
page of a textbook.
d) The number of students who will get financial
assistance in a group of 50 randomly selected students.
