ISYE 6644 MIDTERM EXAM 2024 NEWEST
ACTUAL EXAM COMPLETE ACCURATE
EXAM QUESTIONS WITH DETAILED
VERIFIED ANSWERS (100% CORRECT
ANSWERS) /ALREADY GRADED A+
If X is a continuous variable with c.d.f. F(x), what's
the distribution of F(X)? - ....ANSWER...Unif(0,1).
Inverse transform theorem.
If U is a Unif(0,1) random variable, what's the
distribution of -1/lambda(ln(1-U))? -
....ANSWER...Exp(lambda)
If U is a Unif(0,1) random variable, what's the
distribution of 1/3[-ln(U)]^1/2? - ....ANSWER...Weibull,
with parameters lambda =3 and beta =2
TRUE or FALSE? You can find the inverse c.d.f. of the
standard normal distribution in closed form. -
....ANSWER...False. You need to use an
approximation.
,If U is Unif(0,1), what is [6U]? - ....ANSWER...A 6-side
die toss
If U is Unif(0,1), what is [ln(U)/ln(5/6)]? -
....ANSWER...Geom(1/6)
TRUE or FALSE? If you can't find a good theoretical
distribution to model a certain random variable, you
might want to use the empirical distribution of the
data to do so. - ....ANSWER...True
TRUE or FALSE? The convolution method involves
sums of random variables. - ....ANSWER...True
Suppose that U1 and U2 are PRNs. Whats the
distribution of U1 + U2? -
....ANSWER...Triangular(0,1,2)
YES or NO? As in the notes, suppose that I want to
generate a simple Unif(2/3,1) via A-R. Suppose I
generate a PRN U1 = 0.16. Do I accept U1 as my
Unif(2/3,1)? - ....ANSWER...No. In this example, we
, only accept U1 >= 2/3; so we reject and try again until
we meet that condition.
TRUE or FALSE? The proof that A-R works is really
easy. - ....ANSWER...False
Suppose that X is a continuous RV with p.d.f. f(x) =
30x^4(1-x) for 0<x<1. Why is acceptance-rejection a
good method to use to generate X? -
....ANSWER...Because the c.d.f. of X is very hard to
invert.
Unif(0,1) PRNs can be used to generate which of the
following random entities? -
....ANSWER...Exp(lambda) random variates, Nor(0,1)
random variates, Triangular random variates,
Bern(p) random variates, Nonhomogeneous Poisson
processes, and just about anything else.
If X is an Exp(lambda) random variable with c.d.f.
F(x) = 1-e^(-lambdax), what's the distribution of the
random variable 1-e^(-lambdaX)? -
....ANSWER...Unif(0,1). Inverse transform theroem.
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