Brainarium

probability mass function (pmf) - ️️p(a) = P(X=a) -The pmf of a discrete random variable gives the probability that the random variable will equal a given value cumulative distribution function - ️️SOS F:R --> [0,1] Bernoulli distribution - ️️success or failure X=1 success X=0 failure P(1) = P(X=1) = P P(0) = P(X=0) = 1-P Binomial distribution - ️️Let X represent the number of successes in n trials X~Bin(n,p) sequence of Bernoullis Geometric distribution - ️️L...

Intersection A ∩ B - ️️the set of outcomes that belong to both A and B occurs if and only if both A and B occur A: event {Born in the first half of the year} B: event {Born in a long month} A ∩ B? - ️️A ∩ B = {Jan, Mar, May} Union A ∪ B - ️️set of outcomes that belongs to either A or B (or both). A ∪ B only occurs if at least one of the events A and B occurs A: event {Born in the first half of the year} B: event {Born in a long month} A ∪ B? - ️️A ∪ B = {Ja...

summation of ar^k from k = 0 to infinity converges to a/(1-r) - ️️Geometric Series summation of x^k/k! from k=0 to infinity = e^x - ️️Exponential Series n! - ️️Ordering n objects n! / (n-k)! - ️️Ordering k out of n objects (n c k) = n!/(n-k)!k! - ️️Choosing k out of n objects P(AB) = P(A|B) x P(B) = P(B|A) x P(A) - ️️Multiplication Rule 2^k month a baby is born has 2^12 possible events - ️️How many subsets does a set with k elements have? i) P(A|B) = P(A) i...

mutually exclusive - ️️two or more events are said to be mutually exclusive when at most one of the events can be true EiEj = ∅ whenever i =/ j which means that the events are disjoint sets partition - ️️collection of subsets. If A is an event, then A and A^c form a partition of Ω De Morgan's Law - ️️the complement of the union of two sets is the intersection of the complements ((A ∪ B)^c = A^cB^c) and VICE VERSA: the complement of the intersection is the union of th...

approximation - ️️you can say "this is the real thing, and this is what were replacing it with refinement - ️️making project more precise altitude - ️️how much specificity heuristic - ️️often useful but not guaranteed to solve a problem discrete sample space - ️️consists of a finite set of outcomes continuous sample space - ️️contains an interval (either finite or infinite) of real numbers event - ️️a subset of a sample space of a random experiment venn di...

Consider two public health programs, A and B. Program A prevents 100 deaths immediately. Program B will prevent 110 deaths but 2 years after now. Then, assuming that there is 5% annual discount rate, Program B is better than Program A. - ️️False In a CEA study, if all variables in the decision tree are represented by probabilities as single numbers, then a Monte Carlo simulation study will always give the same CE ratio with constant mean and standard deviation. - ️️False The order...

Cost-effectiveness analysis is useful when considering two competing programs, one of which(program A) is more effective and less expensive than the other one (program B) - ️️False If program C is less effective and more expensive than a linear combination of program A and program D, and program C is mutually exclusive, then we can eliminate program C. - ️️False If a patient lives for 2 years with a utility of 0.9, 3 years with a utility of 0.5, 4 years with a utility of 1, and th...

Cons of using utilities - ️️Framing effects (prompt wording), preferences may change over time, issue of regret, utility tests almost never give same results, method of assessment for determining the "cutpoints" (indifference thresholds) gives different results What does order of chance nodes not affect/effect - ️️Does not affect the paths and outcomes at the end of the tree, but does affect the probability value alone the branches One-way sensitivity analysis - ️️estimat...

1. Drinks that contain _____ should be avoided for fluid replacement. a. electrolytes b. caffeine c. salt d. sugar - ️️b. caffeine 2. When should a full rehabilitation center be established? a. for any incident occurring in extreme weather b. at all incidents requiring the use of PPE c. at all incidents d. in varies with conditions and the nature of the incident - ️️b. at all incidents requiring the use of PPE 3. How are rehabilitation concerns affected by cold weather? a. re...

1. Which type of company specializes in saving victims from fires, confined spaces, trenches, and high angle situations? a. Rescue b. Rapid Intervention c. Truck d. Engine - ️️a. Rescue 2. NFPA standards are ________. a. regulatory law b. administrative law c. consensus documents d. model codes - ️️c. consensus documents 3. Truck companies are sometimes referred to as ______ companies. a. rapid intervention b. rescue c. ladder 4. e - ️️c. Ladder 5. For whom should fir...

1. Which NFPA standard covers wildland fire fighter professional qualifications? a. 1051 b. 1021 c. 1041 d. 1031 - ️️a. 1051 2. What is the term for the burned area of a wildland fire? a. body b. black c. heel d. island - ️️b. black 3. What does the "E" in LCES stand for? a. Escape routes b. Expect surprises c. Establish accountability d. Establish lookouts - ️️a. Escape routes (Lookout, Communications, Escape route, Safety zone) 4. What is the term for the capa...

1. Which term means the amount of energy in a body or stream of water? a. flow b. volume c. watts d. pressure - ️️d. pressure 2. A Pitot gauge is used to determine ________ pressure. a. flow b. operating c. residual d. static - ️️a. flow 3. What is the fastest way for a mobile water supply apparatus to offload water into a portable tank? a. use the dump valve b. connect to the drafting pumper c. use large-diameter hose d. engage the tender's auxiliary pump - ️️a. us...

1. When rescuing a downed fire fighter, what is the first step once the fire fighter is reached? a. attach the downed fire fighter to the RIC-universal air connection b. check the downed fire fighter's air supply c. package the downed fire fighter for removal d. assess the downed fire fighter's condition - ️️d. assess the downed fire fighter's condition 2. When are company officers and safety officers involved in risk-benefit analysis? a. when assigned this task by the incid...

1. How often should ground ladders be visually inspected? a. annually b. biannually c. monthly d. quarterly - ️️c. monthly 2. What is the maximum personnel load for a fire service ladder? a. three fire fighters b. two fire fighters and one victim c. one fire fighter plus one victim d. two fire fighters - ️️b. two fire fighter and one victim 3. When raising a ladder, it should be kept a minimum of ____ from power lines. a. 20 ft b. 15 fit c. 10 ft d. 5 ft - ️️c. 10 ft 4...

1. What is a disadvantage of fire resistive construction? a. non fire-resistive structural members b. the lack of built-in fire protection systems c. susceptibility to water change d. difficulty in ventilating the structure - ️️d. difficulty in ventilating the structure 2. Type III construction is usually limited to a maximum height of ____ stories. a. 3 b. 4 c. 2 d. 5 - ️️b. 4 3. Which of the following is one of the three basic roof designs? a. curved b. hip c. gable d. m...

1. How much damage is caused by forcing the locks on double-hung windows? a. moderate b. none c. minor d. extensive - ️️d. extensive 2. Which kind of steel has been specially treated to resist cutting by normal means? a. case hardening b. alloy c. ductile d. tempered - ️️a. case hardening 3. Which tool is part of the "irons"? a. pick head axe b. mallet c. flat-head axe d. pry bar - ️️c. flat-head axe 4. Where are the hinges placed on a casement window? a. side ...

The American with Disabilities Act requires that communications centers be able to receive calls by which medium? a. Walk-in b. Text message c. Radio transmission d. Personal digital assistant (PDA) - ️️b. Text message What does the "D" stand for in "ADA"? a. Disabilities b. Dangerous c. Distressed d. Directional - ️️a. Disabilities Which item is a primary factor in determining which units to send to an incident? a. The time lapse between call receipt and dispatch...

What is the best way to stop the flow of liquefied petroleum (LP) gas into s structure? a. Turn the valve on the meter to the closed position b. Rotate the quarter-turn valve on the supply pipe c. Close the valve on the storage tank d. Disconnect the cylinder - ️️c. Close the valve on the storage tank In which situation should utility company personnel be called to interrupt power from a remote location? a. The building houses multiple living units b. Multiple hose lines are in house...

Which hazardous material is commonly found in vehicle batteries? a. sulfuric acid b. pentaic acid c. hydrofluoric acid d. hydrochloric acid - a. sulfuric acid Which color are the high voltage cables in a hybrid vehicle? a. red b. orange c. red/white d. black/white - b. orange Which cancer causing material do transformers contain? a. polyphenyl chlorinates b. polychlorinated vinyls c. polychlorinated biphenyls d. biphenyl chlorinates - c. polychlorinated biphenyls A vehicle fueled ...

FANUC EXAM BUNDLE, GRADED A+