ISYE 6402 Midterm Prep QUESTIONS AND CORRECT
DETAILED ANSWERS WITH RATIONALES (100%
CORRECT VERIFIED SOLUTIONS) CURRENTLY
UPDATED VERSION 2026 EDITION |GUARANTEED
PASS
T/F 1. Time series processes generally can be decomposed into a
component modeling systematic variation (trend and seasonality)
and a component modeling stochastic stationary variation.
TRUE! stochastic, like white noise
In mathematics and statistics, a stationary process (a.k.a. a
strict/strictly stationary process or strong/strongly stationary
process) is a stochastic process whose unconditional joint
probability distribution does not change when shifted in time.
Consequently, parameters such as mean and variance also do not
change over time.
T/F Consecutive observations in time series data are independent
and identically distributed.
FALSE - otherwise, you wouldn't have to consider autocorrelation
T/F - Var(a+bY) = b * Var(Y)
FALSE - Var(a+bY) = b^2 * Var(Y)
,T/F - One model for the trend component of a time series is the
simple linear regression model in which time is used as an
explanatory variable.
TRUE
, T/F - If Cov(X,Y)=0 then X and Y are independent
FALSE - If X and Y are independent variables, then their covariance
is 0: Cov(X, Y ) = E(XY ) − µXµY = E(X)E(Y ) − µXµY = 0
The converse, however, is not always true. Cov(X, Y ) can be 0 for
variables that are not independent
T/F If ρ=Corr(X,Y)=0, then X and Y are independent
FALSE - However, if X and Y are uncorrelated, then they can still be
dependent
T/F If X and Y are independent random variables, then we have that
Var(X+Y)≠Var(X)+Var(Y).
FALSE
DETAILED ANSWERS WITH RATIONALES (100%
CORRECT VERIFIED SOLUTIONS) CURRENTLY
UPDATED VERSION 2026 EDITION |GUARANTEED
PASS
T/F 1. Time series processes generally can be decomposed into a
component modeling systematic variation (trend and seasonality)
and a component modeling stochastic stationary variation.
TRUE! stochastic, like white noise
In mathematics and statistics, a stationary process (a.k.a. a
strict/strictly stationary process or strong/strongly stationary
process) is a stochastic process whose unconditional joint
probability distribution does not change when shifted in time.
Consequently, parameters such as mean and variance also do not
change over time.
T/F Consecutive observations in time series data are independent
and identically distributed.
FALSE - otherwise, you wouldn't have to consider autocorrelation
T/F - Var(a+bY) = b * Var(Y)
FALSE - Var(a+bY) = b^2 * Var(Y)
,T/F - One model for the trend component of a time series is the
simple linear regression model in which time is used as an
explanatory variable.
TRUE
, T/F - If Cov(X,Y)=0 then X and Y are independent
FALSE - If X and Y are independent variables, then their covariance
is 0: Cov(X, Y ) = E(XY ) − µXµY = E(X)E(Y ) − µXµY = 0
The converse, however, is not always true. Cov(X, Y ) can be 0 for
variables that are not independent
T/F If ρ=Corr(X,Y)=0, then X and Y are independent
FALSE - However, if X and Y are uncorrelated, then they can still be
dependent
T/F If X and Y are independent random variables, then we have that
Var(X+Y)≠Var(X)+Var(Y).
FALSE
