STATISTICS (STA) 261 FINAL EXAM (ACTUAL 2025/2026)
QUESTIONS AND VERIFIED ANSWERS.(MIAMI UNIVERSITY.)
Ways to determine independence of events - ---Answers-----
1. P(A|B) = P(A)
2. P(B|A) = P(B)
3. P(A&B)= P(A) x P(B)
Random variable - ---Answers-----numerical measurement
of the outcome of a random event
values occur by chance
Probability Distribution of a Random Variable - ---Answers---
--A list of all possible values and their corresponding
probabilities
Expected value of the probability distribution of a random
variable - ---Answers-----describes the center, the long run
average of all values after many trials
Probability distribution of categorical variables - ---Answers-
----used with only 2 categories, 0=failure, 1=success, mean is
probability of success
Normal distribution - ---Answers-----used for continuous
random variables, defined by mean and standard deviation
,symmetric and bell-shaped
Binomial Distribution - ---Answers-----fixed number of trials
2 possible outcomes
Probability of success is the same each trial
independent
Population distribution - ---Answers-----almost never
observed, includes all people and subjects
Sample distribution - ---Answers-----should resemble the
population distribution
consists of data observed and analyzed
Sampling distribution - ---Answers-----long-run behavior of
the statistic
specifies probability of the statistic for a sample given size
P hat - ---Answers-----the sample proportions of successes
in a sample of size n from a population with true proportions p
Mean and St. deviation of p-hat - ---Answers-----Mean- p
St. dev- Sqrt (p x (1-p)/n)
, x-bar - ---Answers-----the mean of observations in SRS of
size n from a population with mean M and standard deviation
sigma
Mean and st.dev of x-bar - ---Answers-----Mean- M
St. dev- sigma/ sqrt(n)
Parameter Variables - ---Answers-----M= population mean
p= population proportion
Sigma= population st.dev
Statistic Variables - ---Answers-----x-bar= sample mean
p-hat= sample proportion
sigma= sample st.dev
Statistical inference - ---Answers-----uses sample data to
draw conclusion on population
uses probability calculations on a sampling distribution of a
statistic
Point estimate - ---Answers-----single number that is our
best guess for the parameter
Interval estimate - ---Answers-----range of plausible values
for the parameter
QUESTIONS AND VERIFIED ANSWERS.(MIAMI UNIVERSITY.)
Ways to determine independence of events - ---Answers-----
1. P(A|B) = P(A)
2. P(B|A) = P(B)
3. P(A&B)= P(A) x P(B)
Random variable - ---Answers-----numerical measurement
of the outcome of a random event
values occur by chance
Probability Distribution of a Random Variable - ---Answers---
--A list of all possible values and their corresponding
probabilities
Expected value of the probability distribution of a random
variable - ---Answers-----describes the center, the long run
average of all values after many trials
Probability distribution of categorical variables - ---Answers-
----used with only 2 categories, 0=failure, 1=success, mean is
probability of success
Normal distribution - ---Answers-----used for continuous
random variables, defined by mean and standard deviation
,symmetric and bell-shaped
Binomial Distribution - ---Answers-----fixed number of trials
2 possible outcomes
Probability of success is the same each trial
independent
Population distribution - ---Answers-----almost never
observed, includes all people and subjects
Sample distribution - ---Answers-----should resemble the
population distribution
consists of data observed and analyzed
Sampling distribution - ---Answers-----long-run behavior of
the statistic
specifies probability of the statistic for a sample given size
P hat - ---Answers-----the sample proportions of successes
in a sample of size n from a population with true proportions p
Mean and St. deviation of p-hat - ---Answers-----Mean- p
St. dev- Sqrt (p x (1-p)/n)
, x-bar - ---Answers-----the mean of observations in SRS of
size n from a population with mean M and standard deviation
sigma
Mean and st.dev of x-bar - ---Answers-----Mean- M
St. dev- sigma/ sqrt(n)
Parameter Variables - ---Answers-----M= population mean
p= population proportion
Sigma= population st.dev
Statistic Variables - ---Answers-----x-bar= sample mean
p-hat= sample proportion
sigma= sample st.dev
Statistical inference - ---Answers-----uses sample data to
draw conclusion on population
uses probability calculations on a sampling distribution of a
statistic
Point estimate - ---Answers-----single number that is our
best guess for the parameter
Interval estimate - ---Answers-----range of plausible values
for the parameter
