Intro to Quant Deck

Question 1

What is a Random Varriable

Answer 1

Experimental outcomes of a random process represented by varriables - assume numerical values

Question 2

What is an example of a random varriable

Answer 2

Coin toss, number of people arriving at Starbucks between 9am and 10am, if we will get rain tomorrow

Question 3

What are types of Random Varriables

Answer 3

Discrete and Continuous

Question 4

What is Discrete Variable

Answer 4

A discrete random variable takes on a countable number of distinct values. Values are finite or countably infinite (e.g.,
0,1,2,….)
Probabilities are assigned to individual values and are often represented using a probability mass function (PMF).
The sum of all probabilities equals
1

Question 5

Is the number of phone calls between 9 and 9:01am discrete or continuous?

Answer 5

Discrete

Question 6

Is the number of products produced by a
machine in one hour discrete or continuous?

Answer 6

Discrete

Question 7

Is the exact height of students in this class discrete or continuous?

Answer 7

Continuous

Question 8

Is the Exact time it takes for participants to finish in a training exercise discrete or continuous?

Answer 8

Continuous

Question 9

What are the discrete probability distributions

Answer 9

Uniform Distribution, Binomial Distribution, Poisson Distribution

Question 10

What is the uniform distribution

Answer 10

n = outcomes, each with probability 1/n – because if it is rolling a dice with 6 sides then you would divide 1/6 to see the equal probability of you getting a certain number

Question 11

Binomial Distribution

Answer 11

Experiment consists of n identical trials
Trial Result: Occurence (success) or non-occurence (failure)
Probability of occurrence on each trial is p

Question 12

What does x = in the binomial distribution

Answer 12

the total number of successes or occurrences, has binomial distribution

Question 13

What is poisson Distribution

Answer 13

Probability of number of events occurring in a fixed interval of time and/or space

The probability of occurrence is the same for any intervals equal length

The occurrence in any interval is independent of an occurrence in any non-overlapping interval

Question 14

Number of patients visiting an emergency room between 11AM and noon - what type of distribution is this

Answer 14

Poisson Distribution

Question 15

Frequency of operation losses in a period of time – what distribution is this any why

Answer 15

Poisson Distribution

Question 16

Number of customers arriving in a bank

Answer 16

Poisson Distribution

Question 17

An average of 15 aircraft accidents occur each year. What is the probability that the 10 accidents will happen next year?

Answer 17

Poisson Distribution Example

Question 18

Experience has shown that 30% of all persons afflicted by a certain
illness recover. A drug company has developed a new medication.
Ten people with the illness were selected at random and injected
with the medication.

Nine of ten injected with the medication recover. Do we believe the
medication works? Why?

Answer 18

Binomial

Question 19

An average of 15 aircraft accidents occur each. What is the probability that less than 10 accidents will happen next year?

Answer 19

Poisson Distribution Example

Question 20

What is a continuous RV?

Answer 20

A continuous random varriable is a random variable where the data can take infinitely many values

Question 21

What is the temperature of a cup of coffee or weights of students in this class– what is that an example of?

Answer 21

Continuous RV

Question 22

What are the continuous probability distributions

Answer 22

Continuous uniform distribution, exponential distribution, normal distribution

Question 23

Suppose you arrive randomly at a bus stop every
morning, between 7:01 and 7:15.

The bus schedule is that it arrives every 10 minutes
(7:00, 7:10, 7:20)

What is the probability that you will wait more than 5 minutes?

Answer 23

Continuous uniform distribution

Question 24

What is exponential distribution

Answer 24

Useful in describing the time or space between events

Question 25

Time between vehicle arrivals at a gate check Time required to complete a questionnaire Distance between major defects in a highway Waiting line applications – time between customers -- what distribution is this

Answer 25

Continuous exponential distribution

Question 26

What is the relationship between Poisson and Exponential?

Answer 26

If number of arrivals per unit time is Poisson, then time between arrival is exponential.

Question 27

What is hypothesis testing

Answer 27

Statistical procedure used to provide evidence in favor of some statement. the likelihood that the result you see occurred by chance and not due to real statistical differences to determine whether there is enough evidence in a sample of data to infer that a certain condition is true for the entire population.

Question 28

What is the null hypothesis H0

Answer 28

statement of the basic proposition being tested

Question 29

What is the Alternative hypothesis Ha

Answer 29

is an alternative accepted only if there is convincing sample evidence it is true

Question 30

What decisions do you decide for the null hypothesis

Answer 30

-Do not reject (Fail to reject) Ho, or reject

Question 31

What do you do to test the hypothesis

Answer 31

Use the test statistic EX: z or t test

Question 32

What does the test statistic tell us?

Answer 32

Calculated difference between means represented in units of standard deviation (two sample) OR How many standard deviations away from the population mean is the sample mean (one sample) The farther away i.e., the larger the test statistic value, the stronger evidence there is to reject the null hypothesis. Choose a confidence level – test statistic above that level means reject the null.

Question 33

When do you use the z-test

Answer 33

n (population is more than or equal to 30) -- any distribution

Question 34

When do you use a t-test

Answer 34

normal distribution and n<30

Question 35

when do you use the z test for proportions

Answer 35

n proportions is less than or equal to 10 and n(1-p) less than or equal to 10