Question

Identify the set of possible values for each random variable. (Make a reasonable estimate based on experience, where necessary, it's not the numbers but the concept that is important.)
a. The number of heads in two tosses of a coin.
b. The average weight of newborn babies born in a particular county one month.
c. The amount of liquid in a 12-ounce can of soft drink.
d. The number of games in the next World Series (best of up to seven games).
e. The number of coins that match when three coins are tossed at once.

Answer 1

a. The number of heads in two tosses of a coin:

In this case number of sample space S = { HH, HT, TH, TT }

Thus, the cases for heads:

It is a discrete random variable.

Number of heads	Cases
0	{ TT }
1	{ HT, TH }
2	{ HH }

b. The average weight of new born babies born in a particular county one month:

The average number weight of new born babies’ possible values contains a whole interval of numbers.

The exact number of babies can take any value in the interval lets say in the interval (a,b)

              It is a continuous random variable.

c. The amount of liquid in a 12-ounce can of soft drink:

The liquid can not take discrete values. The precise value can be any smaller measurement.

The exact amount of liquid can take any value in the interval let’s say in the interval (a,b).

It is a continuous random variable.

d. The number of games in the next World Series (best of up to seven games):

It can be only natural number. It is not possible that it could be 1.5, 2.5 or so.

It must be natural numbers.

It is a discrete random variable.

e. The number of coins that match when three coins are tossed at once.

              Since there are 3 coins, 2 of them can match or 3 of them can also match.

{ 2 , 3}

It is a discrete random variable.