Download EXERCISES: Do all the exercises by writing (unless otherwise

EXERCISES:
Do all the exercises by writing (unless otherwise specified).
If an exercise asks you to ‘state something,’ write it precisely and concisely with
one sentence (unless otherwise specified, of course).
If an exercise asks you to ‘give something,’ write it out but it does not have to be
one sentence. It could be a line or words.
If an exercise asks you to ‘find something,’ it is generally a computational exercise.
Give two things that constitute a probability distribution.
State what a probability distribution indicates.
Give two kinds of probability distributions.
State what a Bernoulli distribution is.
State the condition that makes a Bernoulli distribution a discrete uniform
distribution.
State what a binomial distribution is.
State the condition that makes a binomial distribution a Bernoulli distribution.
State two conditions that make a binomial distribution a discrete uniform
distribution.
If a binomial distribution is a discrete uniform distribution, then it must be a
Bernoulli distribution as well. True or false?
State what μ is. Be more specific than the center or middle of outcomes.
What is the difference between X~Uniform[2, 4] and X~Uniform{2, 3, 4}?
State what a sampling probability distribution is.
State what an underlying probability sampling distribution is.
State the reason why P({4}) = 1/6 for the underlying distribution discussed in this
section.
State what a discrete uniform distribution is.
If a discrete uniform distribution has eight outcomes, then what is the probability
for each of the eight outcomes (sample points).
Give the shape of a Normal distribution.
State the Central Limit Theorem.
State what a Normal distribution is.
State what a bell shape means.
Give the two parameters come with a Normal distribution.
State what the first parameter of a Normal distribution does to the distribution.
State what the second parameter of a Normal distribution does to the shape of the
distribution.
State the reason why μ must be between the minimum and maximum outcomes.
For continuous outcomes, state what indicates probability.
State what the standard Normal distribution is.
Give what Z is.
State what a random variable is.
State what X~Uniform[-3, 9] means.
State what Student’s t distribution is.
State what the asymptotic Normality of the Student’s t distribution is.
State what the Normal standardization of a Normal distribution is.
Give two mathematical operations for the Normal standardization in the order.
Find μ for a probability distribution of P({3}) = 0.1, P({4}) = 0.4, P({5}) = 0.4 and
P({6}) = 0.1.
Find μ for a probability distribution of P({1}) = 0.1, P({4}) = 0.4, P({9}) = 0.4 and
P({16}) = 0.1.
Find μ for a probability distribution of P({3}) = 0.1, P({4}) = 0.2, P({5}) = 0.1 and
P({6}) = 0.5.
Find μ a probability distribution of P({-9}) = 0.1, P({-3}) = 0.4, P({2}) = 0.4 and
P({4}) = 0.1
From the underlying probability distribution of P(2) = 0.2, P(4) = 0.6, and P(8) =
0.2, find the sampling probability distribution of the sample average computed
from a sample of size 2, with replacement.
Give the sample space of the underlying probability distribution in the last exercise.
Give the sample space of the sampling probability distribution in the second last
exercise.
Compute μ of the underlying probability distribution in the third last exercise.
Compute μ of the sampling probability distribution in the fourth last exercise
State what a discrete probability distribution is.
State what a continuous probability distribution is.
Copyrighted by Michael G. Lee, 2012