Review of Poisson and Random Variables

Flashcards about Discrete and Continuous Random variables

What distribution should be used to model the number of defects on a computer if the average of defects is 0.7 per computer?

Poisson distribution with a mean of 0.7.

If one computer is randomly checked, what's the probability that there are no defects (given the average is 0.7 defects per computer)?

P(X=0) = e^(-0.7) ≈ 0.4966

If 3 computers are randomly checked, what distribution would the number of defects found follow?

Poisson distribution.

What is the difference between discrete and continuous random variables?

Discrete random variables have countable values; continuous random variables have uncountably infinite possible values.

What does the area under a PDF (Probability Density Function) represent?

Probability as areas.

For a continuous random variable, what is the probability that X equals a specific value x?

P(X=x) = 0

How to calculate the value of constant C for a valid PDF?

The integral of f(x) over the support must be equal to 1.

If you don't finish eating chicken in 5 minutes and pay 20, otherwise pay 0, is the random variable Y (the amount you pay) discrete or continuous?

Discrete.

How to calculate expected value of Y?

E[Y] = Σ y * P(Y=y)

What is Expected Value?

The expected value (mean) of a random variable. It can be calculated as E[X] = Σ [x * P(X=x)] for discrete variables and E[X] = ∫ [x * f(x) dx] for continuous variables.

What is Variance?

A metric that is used to measure the spread of values in a probability distribution. It's represented as Var(X) = E[X^2] - (E[X])^2.

What is Standard Deviation?

A metric to measure the spread of data. It is mathematically the square root of the variance.

What is a Poisson process?

A model where, in a given set time, some number of events occur. Each event is independent and the rate at which these events occur follows a poisson distribution.

When are trials considered to be Bernoulli Trials (hint: 4 properties)?

Events are mutually exclusive, the trials are independent, the probability of success is constant, and there are a fixed number of trials.