Topic 3

Question 1

a function that associates a real number with each element in the sample space

Answer 1

Random Variable

Question 2

a value of assigned to finite or countably infinite set

Answer 2

Discrete Random Variable

Question 3

a chart or list that shows all the possible outcomes of an event and how likely each one is to happen

Answer 3

Probability Distribution

Question 4

a function that provides the probabilities of occurrence of different possible outcomes in a statistical experiment

Answer 4

Probability Distribution

Question 5

Probability Distribution of a Discrete Random Variable is called

Answer 5

Probability Mass Function (pmf)

Question 6

cumulative distribution function of a real-valued random variable,

Answer 6

Cumulative Distribution Function

Question 6

long term average/mean value of a random variable

Answer 6

Expected Value 𝑬(𝑿)

Question 7

shows how far data in a set are from the mean

Answer 7

Variance

Question 8

a measure that describes the degree to which two random variables change together

Answer 8

Covariance

Question 9

A fixed number of Bernoulli trial

Answer 9

Binomial Distribution

Question 10

Consisting of repeated trials having two possible outcomes (success or failure)

Answer 10

Binomial Distribution

Question 11

Bernoulli Process Properties

Answer 11

1. Experiment consists of repeated trials.
2. Has two outcomes
3. Constant probability
4. Repeated trials are independent

Question 12

A trial have more than two possible outcomes

Answer 12

Multinomial Distribution

Question 13

An experiment yielding numerical values of a random variable, the number of outcomes occurring during a given time interval or in a specified region

Answer 13

Poisson Experiment

Question 14

Poisson Process Properties

Answer 14

1. The number of outcomes occurring in one time interval or specified region of space is
   independent of the number that occur in any other disjoint time interval or region.
2. The probability that a single outcome will occur during a very short time interval or in a small region is proportional to the length of the time interval or the size of the region and does not depend on the number of outcomes occurring outside this time interval or region.
3. The probability that more than one outcome will occur in such a short time interval or fall in such a small region is negligible.

Question 15

No memory

Answer 15

Poisson Process