STA 261 EXAM STUDY QUESTIONS AND
CORRECT ANSWERS!!
A variable X is a _________________ if the value that it assumes, corresponding to the
outcome of an experiment, is a chance or random event.
random variable
. Quantitative random variables are classified as either ______________ or
______________ , according to the values that X can assume.
discrete continuous
We defined probability as the limiting value of the ____________________________ as the
experiment is repeated over and over again.
relative frequency
Now we define the probability distribution for a random variable X as the
____________________________________ distribution constructed for the entire
population of measurements.
relative frequency
The ________________________ for a discrete random variable is a formula, table, or
graph that gives all the possible values of X, and the probability p(x) = P(X=x) associated
with each value x.
probability distribution
A. Requirements for a Discrete Probability Distribution: _______ ≤ D(x) ≤ _______
01
B. Requirements for a Discrete Probability Distribution: ΣD(x) = ___________
1
Toss two fair coins and let X equal the number of heads observed. Find the probability
distribution for X. P(X=0) = ________, P(X=1) = ________, P(X=2) = ________
, 1/4 1/2 1/4
The difference is that the relative frequency distribution describes a _____________ of n
measurements, while the probability distribution is constructed as a model for the entire
_____________ of measurements.
sample population
The population mean, which measures the average value of X in the population, is also
called the expected value of the random variable X and is written as _________ (sometimes
μ). It is the value that you would expect to observe ___________ if the experiment is
repeated over and over again.
E(X) on average
Let X be a discrete random variable with probability distribution p(.). The mean or
___________________ of X is given as μ = E(X) = Σx p(x), summing over all the values of X.
expected value
Let X be a discrete random variable with probability distribution p(.) and mean μ. The
__________________ of X is σ² = Σ(x − μ)² p(x), summing over all values of X.
variance
. The standard deviation σ of a random variable X is equal to the positive _____________ of
its variance.
square root
195a. The expected value of the distribution is ___________________
195b. The variance of the distribution is ___________________
195c. The standard deviation of the distribution is ___________________
a μ = E(X)
b σ² = Σ(x − μ)²·P(x)
c σ = √σ²
CORRECT ANSWERS!!
A variable X is a _________________ if the value that it assumes, corresponding to the
outcome of an experiment, is a chance or random event.
random variable
. Quantitative random variables are classified as either ______________ or
______________ , according to the values that X can assume.
discrete continuous
We defined probability as the limiting value of the ____________________________ as the
experiment is repeated over and over again.
relative frequency
Now we define the probability distribution for a random variable X as the
____________________________________ distribution constructed for the entire
population of measurements.
relative frequency
The ________________________ for a discrete random variable is a formula, table, or
graph that gives all the possible values of X, and the probability p(x) = P(X=x) associated
with each value x.
probability distribution
A. Requirements for a Discrete Probability Distribution: _______ ≤ D(x) ≤ _______
01
B. Requirements for a Discrete Probability Distribution: ΣD(x) = ___________
1
Toss two fair coins and let X equal the number of heads observed. Find the probability
distribution for X. P(X=0) = ________, P(X=1) = ________, P(X=2) = ________
, 1/4 1/2 1/4
The difference is that the relative frequency distribution describes a _____________ of n
measurements, while the probability distribution is constructed as a model for the entire
_____________ of measurements.
sample population
The population mean, which measures the average value of X in the population, is also
called the expected value of the random variable X and is written as _________ (sometimes
μ). It is the value that you would expect to observe ___________ if the experiment is
repeated over and over again.
E(X) on average
Let X be a discrete random variable with probability distribution p(.). The mean or
___________________ of X is given as μ = E(X) = Σx p(x), summing over all the values of X.
expected value
Let X be a discrete random variable with probability distribution p(.) and mean μ. The
__________________ of X is σ² = Σ(x − μ)² p(x), summing over all values of X.
variance
. The standard deviation σ of a random variable X is equal to the positive _____________ of
its variance.
square root
195a. The expected value of the distribution is ___________________
195b. The variance of the distribution is ___________________
195c. The standard deviation of the distribution is ___________________
a μ = E(X)
b σ² = Σ(x − μ)²·P(x)
c σ = √σ²
