What does PMF look like?
A PMF equation looks like this: P(X = x). That just means “the probability that X takes on some value x”. It’s not a very useful equation on its own; What’s more useful is an equation that tells you the probability of some individual event happening.
What values can a discrete random variable take on?
A discrete random variable is one which may take on only a countable number of distinct values such as 0,1,2,3,4,…….. Discrete random variables are usually (but not necessarily) counts. If a random variable can take only a finite number of distinct values, then it must be discrete.
Is the PMF the same as the probability distribution?
Fig.3.1 – PMF for random Variable X in Example 3.3. For discrete random variables, the PMF is also called the probability distribution. Thus, when asked to find the probability distribution of a discrete random variable X, we can do this by finding its PMF.
How to calculate the PMF of a random variable?
Here’s a simple example. The random variable X takes the values 2, 3, 4, and 5 with the probabilities given in the figure, and Y is the function indicated here. Then, for example, the probability that Y takes a value of 4. This is also the value of the PMF of Y evaluated at 4.
Which is the sample space of the PMF?
Here, our sample space is given by S = { H H, H T, T H, T T }. The number of heads will be 0, 1 or 2. Thus R X = { 0, 1, 2 }. Since this is a finite (and thus a countable) set, the random variable X is a discrete random variable.
Which is implicit in the definition of a PMF?
Implicit in the definition of a pmf is the assumption that it equals 0 for all real numbers that are not possible values of the discrete random variable, which should make sense since the random variable will never equal that value. However, cdf’s, for both discrete and continuous random variables, are defined for all real numbers.