Stats - Statistical Distributions
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Flashcards
What is a random variable?
A variable whose value depends on the outcome of a random event.
What is the notation for a random variable?
Capital letters, $X$.
What is the notation for the random variable $X$ taking a particular value $x$?
Can you explain $P(X = x)
The probability that the outcome of the random variable $X$ was the specific outcome $x$.
What’s the shorthand for $P(X = heads)$?
What is a discrete uniform distribution?
A distribution that can only take specific values, which all have the same probability for each outcome.
What is a piecewise function?
We choose the function from a list depending on the input.
What is $P(X = 2)$?
What is $P(X = 2)$?
What is $P(X = 3)$?
What is $P(X = 3)$?What is the advantage of writing probability distributions as a function?
You can have a rule or expression based on the outcome.
What is the advantageo f writing probability distributions as a table?
It’s easier to see the probability for each outcome.
What is the underlying sample space for $X$, the number of heads when three coins are tossed?
What was the head of the table be for the probability distribution of $X$, the number of heads when three coins are tossed?
Number of heads, $x$.
In a probability distribution table where all possible outcomes are listed, what must the sum of all probabilities equal?
What would that notation for “the sum of all probabilities”?
What is $P(X > 3)$?
What is $P(X > 3)$?For a discrete random variable, what is $p(x)$ called?
The probability mass function.
Why is $p(x)$ called a probability mass function for a discrete random variable?
Because the probability of each outcome represents an actual amount of the overall probability.
Visualise what the graphical probability distribution would look like for a six-sided die?
2022-06-02
“Helen believes that the random variable C, representing cloud cover from the large data set, can be modelled by a discrete uniform distribution” How could you write down the probability distribution?
Use the fact that cloud cover can only be one of 9 possible values, so the probability of each case is $\frac{1}{9}$.