Back to Define a random variable and graph its distribution — Problem 4 · Task Set 27

Exercises: Define a Random Variable and Graph Its Probability Distribution

Work through each section in order. A random variable X is a rule that assigns a NUMBER to each outcome in a sample space. To build its probability distribution, group the outcomes by the value of X and add the probabilities in each group; the probabilities of all values must sum to 1. Write probabilities as fractions or decimals. For explanation problems, use complete sentences. Do NOT compute expected value — that comes next lesson.

Grade 11·19 problems·~35 min·Common Core Math - HS Statistics and Probability·group·hss-md-a-1

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Fluency Practice

Build distributions by grouping outcomes by value and summing probabilities.

A family has three children; the eight equally likely outcomes give the number of girls $X$ this distribution:

Value $x$	0	1	2	3
$P(X = x)$	$\frac{1}{8}$	$\frac{3}{8}$	$\frac{3}{8}$	$\frac{1}{8}$

Which check confirms this is a valid probability distribution?

The probabilities sum to $1$ : $\frac{1}{8} + \frac{3}{8} + \frac{3}{8} + \frac{1}{8} = \frac{8}{8} = 1$ .

The values $0, 1, 2, 3$ sum to $6$ .

The largest probability is $\frac{3}{8}$ , which is less than $1$ .

There are four different values of $X$ .