ISYE 6402 Module 1 Questions with Detailed
Verified and 100% Accurate Solutions
What does the Moments of Distribution do?
Moments are a set of statistical parameters to measure and fully characterize a distribution
What are the 4 central moments? (in order)
1. Expectation
2. Variance
3. Skewness
4. Kurtosis
Expectation
the first moment
variance
second central moment
skewness
third central moment, measuring how symmetric the distribution of x is
kurtosis
4th central moment, measuring how fat the tails of the distribution are.
The mean and variance are usually ________ of a distribution.
parameters
,The skewness and kurtosis are__________ _________ of a distribution.
statistical summaries
What are the two common approaches in statistics to obtain estimates for statistical
estimation?
Method of Moments and Maximum Likelihood Approach
Because the estimators of a parameter or statistical summaries are functions of the random
data they are also ____________ ________.
random variables.
Central Limit Theorem (CLT)
Even if the data is not normal, for a large sample size the distribution of x is approximately
normal according to this theory.
S^2 (sample estimator for the variance), what is the distribution and DOF?
Chi-square with n-1 DOF
What are two properties of the statistical estimators?
Unbiasedness and Consistency
Unbiasedness
refers to the property of an estimator that an expectation is exactly equal to the true parameter
Consistency
, for a large sample of data, the estimator is similar to the true parameter, where similarity is in a
probabilistic sense
The likelihood function is a function of.....
theta
is the likelihood function a joint, marginal or conditional distribution?
joint distribution
joint distribution =
conditional x marginal
if X and Y are independent, then the conditional distribution f(x|y) is....
the marginal distribution of x
if X and Y are independent, then the conditional distribution f(y|x) is....
the marginal of y
what are the two types of ways we can make statistical inference?
hypothesis testing and confidence interval
two types of hypothesis testing
parameter-based and distribution-based
Example of parameter-based hypothesis test
H0: theta = estimated theta vs HA: theta =/= estimated theta
Example of distribution-based hypothesis test
Verified and 100% Accurate Solutions
What does the Moments of Distribution do?
Moments are a set of statistical parameters to measure and fully characterize a distribution
What are the 4 central moments? (in order)
1. Expectation
2. Variance
3. Skewness
4. Kurtosis
Expectation
the first moment
variance
second central moment
skewness
third central moment, measuring how symmetric the distribution of x is
kurtosis
4th central moment, measuring how fat the tails of the distribution are.
The mean and variance are usually ________ of a distribution.
parameters
,The skewness and kurtosis are__________ _________ of a distribution.
statistical summaries
What are the two common approaches in statistics to obtain estimates for statistical
estimation?
Method of Moments and Maximum Likelihood Approach
Because the estimators of a parameter or statistical summaries are functions of the random
data they are also ____________ ________.
random variables.
Central Limit Theorem (CLT)
Even if the data is not normal, for a large sample size the distribution of x is approximately
normal according to this theory.
S^2 (sample estimator for the variance), what is the distribution and DOF?
Chi-square with n-1 DOF
What are two properties of the statistical estimators?
Unbiasedness and Consistency
Unbiasedness
refers to the property of an estimator that an expectation is exactly equal to the true parameter
Consistency
, for a large sample of data, the estimator is similar to the true parameter, where similarity is in a
probabilistic sense
The likelihood function is a function of.....
theta
is the likelihood function a joint, marginal or conditional distribution?
joint distribution
joint distribution =
conditional x marginal
if X and Y are independent, then the conditional distribution f(x|y) is....
the marginal distribution of x
if X and Y are independent, then the conditional distribution f(y|x) is....
the marginal of y
what are the two types of ways we can make statistical inference?
hypothesis testing and confidence interval
two types of hypothesis testing
parameter-based and distribution-based
Example of parameter-based hypothesis test
H0: theta = estimated theta vs HA: theta =/= estimated theta
Example of distribution-based hypothesis test
