A discrete random variable takes only specific, countable values: the number of books you read in a month, for example, but never 2.5 books.
Pick a hobby. You'll build its probability distribution, then use it to find the expected value, variance, and standard deviation.
Let X be the number of . Suppose the probability of each value is given by this function:
Fill in the table. Plug each value of x into the function. Enter probabilities as decimals (10% → 0.1).
| x | P(X = x) |
|---|
Each bar is one row of the table. The taller the bar, the more likely that value.
To find the probability that X falls in a range, add up the probabilities of the values in that range.
| x | P(X = x) |
|---|
The expected value E(X) is the average you'd get over many, many repeats. Multiply each value by its probability and add the products:
| x | P(X = x) |
|---|
Variance measures how spread out the distribution is around its expected value. We'll build it one column at a time. First, subtract the mean from each value: x − E(X), where .
| x | P(X = x) | x − E(X) |
|---|
Squaring removes the negative signs, so values below and above the mean both count as spread.
| x | P(X = x) | x − E(X) | (x − E(X))² |
|---|
Multiply each squared deviation by P(X = x). The sum of that column is the variance.
| x | P(X = x) | x − E(X) | (x − E(X))² | (x − E(X))² · P(X = x) |
|---|
What is the variance of X?
What is the standard deviation of X? (Round to two decimal places.)