COMS 5583 EXAM PREPARATION TEST
BANK WITH CORRECT ANSWERS
●● True or False: Simulation can be used to analyze supply-chain
models too complicated to solve analytically.
Answer: True.
●● For bisection, what equation form do you need first?
Answer: Move everything to one side and define g(x)=0.
●● For e^x = x^2, what g(x) should you use for bisection?
Answer: g(x)=e^x - x^2.
●● What does a sign change between g(a) and g(b) tell you in bisection?
Answer: A root lies somewhere in [a,b], assuming g is continuous.
●● In bisection, after checking the midpoint, which interval do you
keep?
Answer: Keep the subinterval where g(x) changes sign.
●● What is Newton's method update formula?
Answer: x_{n+1}=x_n - g(x_n)/g'(x_n).
,●● For conditional probability, what is P(A | B)?
Answer: P(A | B)=P(A ∩ B)/P(B).
●● For continuous conditional probability, how do you compute P(A ∩
B)?
Answer: Integrate the PDF over the interval where both events are true.
●● In the practice problem P(X<1 | X>1/2), what is the numerator
event?
Answer: 1/2 < X < 1.
●● In the practice problem P(X<1 | X>1/2) with support 0<X<2, what is
the denominator event?
Answer: 1/2 < X < 2.
●● Common mistake: Can you cancel x/2 across numerator and
denominator integrals?
Answer: No. Compute each integral separately; do not cancel variable
terms inside integrals.
●● If f(x)=x/2, what is the antiderivative?
Answer: ∫(x/2)dx = x^2/4.
, ●● For the practice conditional probability with f(x)=x/2, what is P(X<1
| X>1/2)?
Answer: 0.2.
●● What distribution models the trial number of the first success?
Answer: Geometric distribution.
●● For Geom(p) counting the successful trial itself, what is P(X=k)?
Answer: (1-p)^{k-1}p.
●● For Geom(p) counting the successful trial itself, what is E[X]?
Answer: 1/p.
●● If each trial succeeds with probability 0.6, what is P(first success on
trial 3)?
Answer: (0.4)^2(0.6)=0.096.
●● In a geometric problem, what does q usually mean?
Answer: q=1-p, the failure probability.
●● For a 10-sided die, what is the success probability of rolling a 5?
Answer: p=1/10.
BANK WITH CORRECT ANSWERS
●● True or False: Simulation can be used to analyze supply-chain
models too complicated to solve analytically.
Answer: True.
●● For bisection, what equation form do you need first?
Answer: Move everything to one side and define g(x)=0.
●● For e^x = x^2, what g(x) should you use for bisection?
Answer: g(x)=e^x - x^2.
●● What does a sign change between g(a) and g(b) tell you in bisection?
Answer: A root lies somewhere in [a,b], assuming g is continuous.
●● In bisection, after checking the midpoint, which interval do you
keep?
Answer: Keep the subinterval where g(x) changes sign.
●● What is Newton's method update formula?
Answer: x_{n+1}=x_n - g(x_n)/g'(x_n).
,●● For conditional probability, what is P(A | B)?
Answer: P(A | B)=P(A ∩ B)/P(B).
●● For continuous conditional probability, how do you compute P(A ∩
B)?
Answer: Integrate the PDF over the interval where both events are true.
●● In the practice problem P(X<1 | X>1/2), what is the numerator
event?
Answer: 1/2 < X < 1.
●● In the practice problem P(X<1 | X>1/2) with support 0<X<2, what is
the denominator event?
Answer: 1/2 < X < 2.
●● Common mistake: Can you cancel x/2 across numerator and
denominator integrals?
Answer: No. Compute each integral separately; do not cancel variable
terms inside integrals.
●● If f(x)=x/2, what is the antiderivative?
Answer: ∫(x/2)dx = x^2/4.
, ●● For the practice conditional probability with f(x)=x/2, what is P(X<1
| X>1/2)?
Answer: 0.2.
●● What distribution models the trial number of the first success?
Answer: Geometric distribution.
●● For Geom(p) counting the successful trial itself, what is P(X=k)?
Answer: (1-p)^{k-1}p.
●● For Geom(p) counting the successful trial itself, what is E[X]?
Answer: 1/p.
●● If each trial succeeds with probability 0.6, what is P(first success on
trial 3)?
Answer: (0.4)^2(0.6)=0.096.
●● In a geometric problem, what does q usually mean?
Answer: q=1-p, the failure probability.
●● For a 10-sided die, what is the success probability of rolling a 5?
Answer: p=1/10.
