Probability Distribution

Probability Distribution

When working with random variables, we can ask questions like "what is the probability that X equals 2 heads in three coin flips, or that Y equals a value greater than 2 on a die roll?". We'll work these example scenarios below.

Example 1

If we flip a coin three times, the sample space will look something like below:

$$S = { HHH, HHT, HTH, HTT, THH, TTH, THT, TTT}$$

Now what is P(X=2)? In other words, what is the probability that X (the number of heads in three coin flips) is exactly equal to two? The outcomes that satisfy exactly two heads include: HHT, HTH and THH. Therefore we can say

$$P(X=$$ ...