Lesson 3: Finding the possible values of a random variable

A ______________________ is a set of possible values from a random experiment. For example, in tossing a coin, we can either get head or tail, such tossing a coin is an experiment where we can give values for such event.

A ______________________ is one that may take on only a countable number of distinct values such as 0,1,2,3,4, etc. This variable is usually (but not necessarily) counts. It is a random variable that can take only a finite number of distinct values.

If a coin is tossed, what are the possible values of the random variable for the number of heads?

• 0, 1

• 0, 1, 2

• 1, 2, 3

• 0, 1, 2, 3

Suppose you tossed two coins.

What are the sample spaces for the experiment above?

• HH, TT

• HH, HT, TT

• HH, TH, TT

• HH, HT, TT, TH

Suppose you tossed two coins.

What are the possible values of the random variable for the number of heads?

• 0,1

• 0,1,2

• 1,2,3

• 0,1,2,3

You decide to conduct a survey of families with two children. You are interested in counting the number of girls (out of 2 children) in each family.

Is the above experiment “counting the number of girls (out of 2 children in each family” a random variable?

• Yes, it is a random variable.

• No, it is not a random variable.

• Maybe.

• It cannot be determined

You decide to conduct a survey of families with two children. You are interested in counting the number of girls (out of 2 children) in each family.

If the experiment above shows a random variable, then what are the possible values of it?

• Its value can be 1 or 2.

• Its value can be 0, 1, or 2.

• Its value can be 2 or 4.

• None, since it is not a random variable.

Suppose two laptops are tested. Let D represent the defective laptop and N represent the non-defective laptop.

What are the possible sample spaces for the experiment?

• DD, NN

• DD, DN, NN

• DD, ND, NN

• DD, DN, NN, ND

Suppose two laptops are tested. Let D represent the defective laptop and N represent the non-defective laptop.

If we let X be the random variable representing the number of defective laptops. What are the possible values of the random variable?

• 0, 1

• 0, 1, 2

• 1, 2, 3

• 0, 1, 2, 3

In a local community, a couple was asked the questions, “Are you satisfied with the work of the current president?” If the husband and the wife both said “yes”, the response is written as YY. If the husband said yes and the wife said “no”, the response is YN. Let X be the number of “yes” responses, what are the possible values of the random variables?

• 0, 1, 2

• 1, 2, 3

• 2, 3, 4

• 1, 1, 2