Download MTH 254 - CALCULUS

MTH 265 - EXAM II REVIEW
Friday, February 11
For this exam you may bring ONE 8.5 inch by 11 inch page of notes (both sides). You may put any
formula on your note page, calculator command, and reminders. You may NOT put examples with
solutions or any of our homework problems with solutions on your page. Inappropriate items on your
formula sheet will be removed before you take your exam.
3.3 Continuous Random Variables
 Be able to find the cumulative distribution
function for a continuous random variable.
See Example 3.22.
 Be able to find the probability of event
occurring for a continuous random variable.
See Example 3.21.
 Be able to find the mean, variance, and
standard deviation for a continuous random
variable from a given experiment. See
Example 3.24.
 Given a cumulative probability distribution
function, be able to use it to find the median
or any percentile.
 Typical and reasonable test questions would
be like problems 1, 7, and 11.
3.4 Functions of Random Variables
 Be able to determine the mean, variance, and
standard deviation of a constant multiple of a
random variable (given the mean and standard
deviation of the random variable). See
example 3.25.
 Be able to determine the mean, variance, and
standard deviation of a linear combination of
a set of independent random variables (given
the mean and standard deviation of the
random variables). See example 3.27.
 Be able to determine the mean, variance, and
standard deviation of the mean of a random
sample from a population with known mean
and standard deviation. See example 3.28.
 Typical and reasonable test questions would
be like problems 1, 3, 5, and 9.
4.1 The Binomial Distribution
 Know what requirements must be fulfilled for
a random variable to be Binomial. See p. 120.
 Be able to find the distribution for a Binomial
random variable (recognize it is Binomial and
find the mean, variance, and standard
deviation). See example 4.1.
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
Be able to calculate probabilities for a
Bernoulli random variable. See example 4.2
through 4.5.
Typical and reasonable test questions would
be like problems 1, 3, 5, 7, and 9.
4.2 The Poisson Distribution
 Be able to find recognize when you have a
Poisson random variable. Clue into the
wording that there is a number of occurrences
of an event in a specified unit (volume, time,
area…).
 Know how to find the mean, variance, and
standard deviation for a Poisson random
variable.
 Be able to determine the parameter, , needed
to specify the Poisson probability distribution.
 Be able to calculate probabilities for a
Poisson random variable using the probability
distribution or using your poissonpdf or
poissoncdf features of your calculator. See
examples 4.6, 4.7, 4.9, 4.10, and 4.11.
 In some circumstances we can use the
Poisson distribution to approximate the
Binomial. If I want you to demonstrate the
ability to do this on the test, I will specifically
tell you to use the Poisson to approximate the
Binomial. See page 127 for an example of
this approximation.
 Typical and reasonable test questions would
be like problems 1, 2, 4, 5, 7 (Poisson
approximation to the Binomial).
4.3 The Normal Distribution
 Know the proportion of any normal
population that is within one, two, or three
standard deviation of the mean. See page
134.
 Be able to calculate the area under the normal
curve (probabilities) for given values of the
standard normal random variable Z. See
example 4.15, 4.16, and 4.17.
 Be able to calculate percentiles for a standard
normal random variable. See example 4.18.
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

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Be able to convert any normal random
variable to a standard normal random variable
by using the z-score. Remember the z-score
tells us how many standard deviations above
or below the mean the value is. See example
4.12 and 4.13.
Be able to calculate probabilities for any
normal random variable given its mean and
standard deviation.
Be able to calculate percentiles for any
normal random variable.
Typical and reasonable test questions would
be like problems1, 3, 5, 7, and 9.
4.5 The Exponential Distribution
 Know when a random variable can be
categorized as an Exponential Random
Variable.
 Know how to use the cumulative Exponential
distribution to calculate probabilities. See
example 4.25.
 Know the mean, variance, and standard
deviation of an Exponential Random
Variable.
 Pay attention to the wording difference when
you are given λ versus when you are given the
mean of an Exponential process. Carefully
read Example 4.26 where the “mean rate of
15 particles per minute” was given and that is
λ. λ is defined as a mean number of
occurrences per unit. If you are given the
mean time until the next occurrence or the
mean lifetime, then that is the mean of the
random variable and NOT λ. See Example
4.27.
 Don’t forget that the Exponential distribution
has no memory, so asking to find the
probability a component lasts two years will
give the same probability as asking to find the
probability that a component lasts two more
years after it already lasted three years.
 Typical and reasonable test questions would
be like problems 1, 2, 3, 4, 5, and 6.
4.8 The Central Limit Theorem
 Be able to use the Central Limit Theorem to
determine the mean, variance, and standard
deviation for the sample mean of a simple


random sample and be able to calculate
probabilities using them. See example 4.31.
Be able to use the normal approximation to
the Binomial and use the continuity
correction. See Example 4.32 and 4.33.
Typical and reasonable test questions would
be like problems 1, 3, 5, and 7.
5.1 Point Estimation
 Know the vocabulary: point estimate,
statistic, parameter, and bias.
5.2 Large-Sample Confidence Intervals for a
Population Mean
 Be able to find confidence intervals for the
mean of a population using a sample from a
population with known mean and standard
deviation. See examples 5.3, 5.2, 5.3, and 5.9.
 Know how to interpret a confidence interval.
Read page182 and 183! See Example 5.7 and
5.8.
 Be able to find the level of a given confidence
interval for the mean of a population. See
example 5.6.
 Be able to find the size of the sample needed
to obtain a given level of confidence for the
mean of a population. See example 5.9.
 Know what the margin of error is and how to
interpret it.
 Typical and reasonable test questions would
be like problems 3, 5, 7, and 9.
5.3 Confidence Intervals for Proportions
 Be able to find two-sided confidence intervals
for the proportion of successes of a
population. Use the formula that appears on
page 190…NOT the one in the box on page
193. See example 5.11.
 Be able to find the size of the sample needed
to obtain a given level of confidence for the
proportion of successes of a population. See
examples 5.12 and 5.13.
 Typical and reasonable test questions would
be like problems 1, 2, 3, and 13.