Lect 21 Flashcards
(23 cards)
What is a discrete probability distribution?
A random variable that takes on only specific values, only whole numbers.
Discrete distributions are used in scenarios where outcomes are countable, such as the number of students in a class.
What is a continuous probability distribution?
A random variable that can take on any value from an interval.
Continuous distributions are used in scenarios where outcomes can be measured, such as height or weight.
Describe discrete probability when we don’t have equally likely outcomes:
Discrete Probability:
• Empirical- Calculated after trials
• Example - non-equally likely outcomes
• P(Event) = number of times Event happened/ number of total trials
Describe discrete probability when we have equally likely outcomes:
Discrete Probability
• Theoretical — Calculated before trials
• Example - equally likely outcomes
• P(Event) = number of ways Event can happen/number of total outcomes
What is the range of any probability?
Between 0 and 1
A probability of 0 indicates an impossible event, while a probability of 1 indicates a certain event.
What does a probability distribution have to list?
A probability distribution have to list every single outcome with no overlap
What can the outcome of each trial in a binomial probability distribution be categorized as?
Success or failure
In a binomial probability distribution, what is the nature of the number of trials?
Fixed number of trials (n)
What must be true about the probability of success in a binomial probability distribution?
The probability of success (p) is the same for each trial
What characteristic defines the independence of trials in a binomial probability distribution?
Each trial is independent of the others
What does P(X=x) represent in the context of binomial probability distribution?
The probability of having x successes
Fill in the blank: In a binomial probability distribution, the outcome of each trial can be categorized as a _______.
Success or failure
True or False: In a binomial probability distribution, the probability of success can vary from trial to trial.
False
What are the four key characteristics of a binomial probability distribution?
- Outcome is success or failure
- Fixed number of trials (n)
- Same probability of success (p) for each trial
- Trials are independent
In a geometric probability distribution, what is true about the probability of success (p)?
It is the same for each trial
What does it mean for trials to be independent in a geometric probability distribution?
Each trial is independent of the others
What does P(X=x) represent in geometric probability distribution?
The probability that the xth trial is the first success
Describe Geometric probability distribution:
Geometric probability distribution:
• The outcome of each trial can be categorized as a success or failure
• The probability of success (p) is the same for each trial
• Each trial is independent of the others
• P(X=x) is the probability the xth trial is the first success
What is a key characteristic of the Poisson Probability Distribution?
There is a fixed interval of time or area or volume, etc.
What does the mean number of times a certain event takes place in a Poisson distribution represent?
It is represented by the symbol м.
In a Poisson distribution, the occurrence of events is _______ of the time the last event took place.
independent
What does P(X=x) represent in the context of the Poisson Probability Distribution?
The probability of having x events take place per interval under consideration.
Describe Poisson Probability Distribution:
Poisson Probability Distribution:
• There is a fixed interval of time or area or volume, etc….
• During this interval there is a mean number of times a certain event takes place (м) which is independent of the time the last such event had taken place
• P(X=x) is the probability of having x events take place per interval under consideration
