MSIS 3223 EXAM QUESTIONS WITH CORRECT ANSWERS
LATEST UPDATE
Classical definition of probability
The process that generates the outcome is known and probabilities can be deduced
from theoretical arguments
Relative frequency definition of probability
based on empirical data. The probability that an outcome will occur is simply the relative
frequency associated with that outcome
Subjective definition of probability
based on judgement and experience
Random variable
A numerical description of the outcome of an experiment. May be continuous or discrete
Discrete random variable
one for which the number of outcomes can be counted
Continuous random variable
has outcomes over one or more continuous intervals or real numbers
Expected value of a random variable
corresponds to the notion of the mean, or average for a sample
How is the variance of a discrete random variable computed?
Weighted average of the squared deviations from the expected value
What does variance measure?
The uncertainty of the random variable
The higher the variance the higher the ______ of the outcome
uncertainty
Normal distribution
A continuous distribution described by the familiar bell shaped curve
What is the normal distribution characterized by?
The mean and the standard deviation
Skewness of a normal distribution
Zero, it is symmetric
The mean, median, and mode of a normal distribution are
all equal
What is the range of X of a normal distribution?
unbounded, meaning that the tails of the distribution extend to negative and positive
infinity
How do the empirical rules apply for the normal distribution?
apply exactly
Probability density functions
the distribution that characterizes outcomes of a continuous random variable
Properties of probability density functions
- A graph of the density function must lie at or above the x-axis
- The total area under the density function above the x-axis is 1
- For continuous random variables, there are an infinite number of values
LATEST UPDATE
Classical definition of probability
The process that generates the outcome is known and probabilities can be deduced
from theoretical arguments
Relative frequency definition of probability
based on empirical data. The probability that an outcome will occur is simply the relative
frequency associated with that outcome
Subjective definition of probability
based on judgement and experience
Random variable
A numerical description of the outcome of an experiment. May be continuous or discrete
Discrete random variable
one for which the number of outcomes can be counted
Continuous random variable
has outcomes over one or more continuous intervals or real numbers
Expected value of a random variable
corresponds to the notion of the mean, or average for a sample
How is the variance of a discrete random variable computed?
Weighted average of the squared deviations from the expected value
What does variance measure?
The uncertainty of the random variable
The higher the variance the higher the ______ of the outcome
uncertainty
Normal distribution
A continuous distribution described by the familiar bell shaped curve
What is the normal distribution characterized by?
The mean and the standard deviation
Skewness of a normal distribution
Zero, it is symmetric
The mean, median, and mode of a normal distribution are
all equal
What is the range of X of a normal distribution?
unbounded, meaning that the tails of the distribution extend to negative and positive
infinity
How do the empirical rules apply for the normal distribution?
apply exactly
Probability density functions
the distribution that characterizes outcomes of a continuous random variable
Properties of probability density functions
- A graph of the density function must lie at or above the x-axis
- The total area under the density function above the x-axis is 1
- For continuous random variables, there are an infinite number of values
