ANSWERS | CERTIFIED
/. What are the three perspectives of probability? - Answer-✅Classical, relative
frequency, subjective
/.What is a random variable? - Answer-✅Numerical description of experiment outcome
/.What is the difference between a discrete and continuous random variable? - Answer-
✅Discrete: countable outcomes, continuous: outcomes over intervals
/.What is the expected value of a random variable? - Answer-✅Corresponds to mean or
average for a sample
/.How do you find joint probabilities? - Answer-✅Multiply the probabilities of the two
events
/.How do you find conditional probabilities? - Answer-✅Divide the joint probability by the
probability of the given event
/.How do you identify that two events are independent? - Answer-✅If the occurrence of
one event does not affect the probability of the other event
/.What is the classical definition of probability? - Answer-✅Probabilities deduced from
theoretical arguments
/.What is the relative frequency definition of probability? - Answer-✅Probabilities based
on empirical data
/.What is the subjective definition of probability? - Answer-✅Probabilities based on
judgment and experience
/.What is the range of probabilities? - Answer-✅Between 0 and 1
/.What is the expected value helpful for? - Answer-✅Making a variety of decisions
/.What is the expected value equivalent to? - Answer-✅Mean or average for a sample
, /.What is the probability of a respondent being female and preferring Science? -
Answer-✅Unknown, not enough information given
/.How can you determine if two events are independent? - Answer-✅If the probability of
one event is not affected by the occurrence of the other event
/.What is the purpose of using a cross-tabulation? - Answer-✅To analyze the
relationship between two variables
/.What is the purpose of finding joint probabilities? - Answer-✅To determine the
probability of two events occurring together
/.What is the purpose of finding conditional probabilities? - Answer-✅To determine the
probability of one event given that another event has occurred
/.What is the weighted average of the squared deviations from the expected value? -
Answer-✅Variance of a discrete random variable.
/.What does the variance measure? - Answer-✅Uncertainty of the random variable.
/.What is the normal distribution? - Answer-✅Continuous distribution described by a
bell-shaped curve.
/.What are the parameters of the normal distribution? - Answer-✅Mean and standard
deviation.
/.What are the properties of the normal distribution? - Answer-✅Symmetric, zero
skewness, mean=median=mode, unbounded range.
/.What are the empirical rules for the normal distribution? - Answer-✅68-95-99.7 rule.
/.What are probability density functions? - Answer-✅Distributions that characterize
outcomes of continuous random variables.
/.What are the properties of probability density functions? - Answer-✅Graph lies at or
above x-axis, total area under the function is 1, infinite number of values.
/.What does a probability density function calculate? - Answer-✅Probability of a random
variable lying within a certain interval.
/.What is regression analysis? - Answer-✅Statistical technique for modeling the
relationship between variables.