In the experiment of flipping a regular coin twice, if the random variable 𝑥 equals the number of heads minus the number of tails, find the range of 𝑥.
In the first coin toss, we have two options, heads or tails. If the first toss is heads, the second toss will be either heads or tails. And if the first toss is tails, the second one will be heads or tails. That means we have four possible outcomes: heads heads, heads tails, tails heads, or tails tails.
We know that 𝑥 equals the number of heads minus the number of tails. For the first option, we have two heads and zero tails. 𝑥 is equal to two minus zero, which equals two. And then we have the case where there is one head and one tails. One minus one equals zero. This is also true if we get tails and then heads, because we’re just subtracting the number of heads and the number of tails. We’re not considering the order they were flipped in.
Our final option has two tails and zero heads, zero minus two, equals negative two. The range of 𝑥 is the set of all possible values 𝑥 can be. Here that would be two, zero, and negative two. The range of 𝑥 is the set negative two, zero, two.