Summary
Summary of Analysis of Production Systems
- Course
- Institution
Summary of the course Analysis of production systems, including information about all the treated slides.
[Show more]
Seller
Follow
lucbeerten
Content preview
Summary Analysis of production Systems[4DC10]
February 11, 2021
Probability models
Probabilities
If two events are independent of each other
P (EF ) = P (E) ∗ P (F )
Conditional probability
P (EF )
P (E|F ) =
P (F )
Expected value
Expected value(Discrete) (centre of probability mass):
∞
X
E[X] = xj ∗ p j
j=1
Sum of expectation is expectation of sum
E[X + Y ] = E[X] + E[Y ]
Rule for constants
E[aX + b] = a ∗ E[X] + b
If two events are independent
E[XY ] = E[X]E[Y ]
Variance
Variance:
V ar[X] = E[X 2 ] − (E[X])2
Standard deviation: p
σ(X) = V ar[X]
Rule for constants
V ar[aX + b] = a2 V [X]
If two events are independent
V ar[X + Y ] = V ar[X] + V ar[Y ]
1
, Continuous random variable
Z b
F (X) = P (a < X < b) = f (y)dy
a
Z ∞
E[X] = x ∗ f (x)dx
−∞
Uniform random variable X on [a, b] has density:
1
f (x) = ,a < x < b
b−a
x−a
P (X ≤ x) = ,a < x < b
b−a
a+b
E[X] =
2
1
V ar[X] = (b − a)2
12
Density
d
f (x) =P (X ≤ x)
dx
Exponential random variable X with parameter(or rate) λ has density
f (x) = λe−λx , x > 0
P (X ≤ x) = 1 − e−λx
1
E[X] =
λ
1
V ar[X] = 2
λ
Binomial
A Binomial random variable X is the number of successes in n independent Bernoulli trials
X1 , ... , Xn , each with probability p of success.
n
P (X = k) = ∗ pk (1 − p)n−k k = 0, 1, ...n
k
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller lucbeerten. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $0.00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
64438 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now