Cogito
Probability and Statistics · Chapter 5 · Lesson 2
Random Variables
A number attached to a random outcome.
12 problems · about 21 minutes · TEKS P.S.2.G, S-MD.A.1
What this lesson teaches
The student builds probability distributions for discrete random variables and computes their mean.
- A random variable assigns a number to each random outcome.
- Its distribution lists every value with its probability, totalling 1.
- Its mean is the expected value: each value times its probability.
Warm Up
Straightforward practice. Get the method working first.
5 problemsProbabilities 0.3, 0.3 and one more. What must it be?
Answer 0.4
Why 0.4.
What is a random variable?
Answer A number attached to each outcome of a random process.
Why A number assigned to each outcome.
Probabilities 0.1, 0.4 and one more. What must it be?
Answer 0.5
Why They total 1.
Values 1 and 3 with probabilities 0.5 each. Mean?
Answer 2
Why 0.5 + 1.5.
Two dice. How many ways to total 7?
Answer 6
Why Six ordered pairs.
Build It Up
The same ideas with more to keep track of.
3 problemsTwo dice. How many ways to total 2?
Answer 1
Why Only 1 and 1.
Number of siblings. Discrete or continuous? 1 discrete, 2 continuous.
Answer 1
Why A count.
Exact height. Discrete or continuous? 1 or 2.
Answer 2
Why Any value in a range.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsWhich must be true of a probability distribution?
Answer The probabilities total 1; Each probability is between 0 and 1
Why A die has mean 3.5, which is not a face.
Values 2 and 6 with probabilities 0.5 each. Mean?
Answer 4
Why 1 + 3.
The Total: A distribution has probabilities 0.2, 0.3 and one unknown. What must the third be?
Answer 0.5
Why 0.5.
The Mean: Values 0, 1, 2 with probabilities 0.25, 0.5, 0.25. What is the mean?
Answer 1
Why 1.