Definitions
What is it called when the outcome of one event does not affect the probability of outcomes in another event?
Independent Events
A quality control manager selects a random sample of 20 manufactured components from a large production line where each component independently has a 3% probability of being defective.
Binomial
n= 20
p = 0.03
What is the correct configuration when calculating using DRVs
1Var XList: ???
1Var Freq: ???
1Var XList: List 1
1Var Freq: List 2
What is the formula for the area of a triangle
A = 1/2 \times base \times height
What is the assumption that we should always use
Assumption of Independence
What is the description of mutually exclusive events?
Two events which cannot occur simultaneously
P(A\cap B)=0
A forestry study records the trunk diameters of mature radiata pine trees. The tree diameters form a mean of 40cm with standard deviation 6cm.
Normal Distribution
\mu = 40
\sigma = 6
SD(A) = 2 and SD(B) = 3
SD(A + B) = 3.606
What is the equation for finding relative risk using conditional probabilites
R.R = (P(A|B))/(P(A|C)
What does the S stand for in the acronym FITS
Same probability of success
How many standard deviations should be distributed across a range of data if it is to be modelled by a normal distribution?
6 standard deviations
(3 either side of the mean)
A call center logs incoming emergency requests. On average, 12 calls arrive per hour.
Poisson
\lambda =12
A DRV has a VAR(2.35).
If a constant (b) of 5 is added to the DRV. What will the new VAR be?
Var(2.35)
Constants do not affect the variance
What both the formulae for proving that two events are independent?
P(A)xxP(B)=P(A\capB)
P(A|B)=P(A)
An internet provider models the number of phone calls to its technical support line between 9:00 AM and 11:00 AM on weekdays using a Poisson distribution. Historical data shows that the support line receives an average of 3 call every 15 minutes.
Constant Rate: Call volume often fluctuates—for example we would expect more calls during a maintenance period or if there was an outage.
Some distributions can be described as continuous while others are discrete, what is the difference between the two?
Discrete: countable value only (Whole numbers)
Continuous: measurable values (Decimal numbers)
A civil engineer estimates the completion time for a bridge repair project based on the engineers experience he indicates that 18 days in most likely. Past projects indicate the time required is strictly between 10 and 30 days.
Triangular
a = 10
b = 30
c = 18
Find the Var(aX) if they sell each soap for $10.
What is the formula for finding \lambda using P(X=0)
\lambda = -ln (P(X=0))
Alex is a basketball player who takes 10 free throw shots during a practice session. Over her past season, her historical free-throw shooting percentage has been 70%
Same Rate of Success: Alex might suffer from fatigue towards the end of the free throws, decreasing their success rate.
If two non-zero probability events are mutually exclusive, what can be definitively concluded about their independence?
They cannot be independent
A commuter arrives at a light rail platform where trains pass every 10 minutes. The passenger arrives randomly and has a equally likely chance of waiting any amount of time between trains.
Uniform
a = 0
b = 10
VAR(A) + Var (B) = Var(A + B)
What is the formula for finding the height of a triangular distribution at point x when x is less than c
h= (2(x-a))/((b-a)(c-a))
Mr. Boon is trying to evaluate the probability that his students success in the up and coming exam. He assumes that YOU are studying hard at home. Is his assumption correct?
Yes of course! All of Mr Boon's students care greatly about their exam grades and are diligently working over the course of many weeks for their exam as they understand that cramming last minute will not lead to desirable grades.