If a coin is flipped and it lands on Heads, y, will the value of the random variable Z be greater than or equal to 0?
To determine if the random variable Z will be greater than or equal to 0 when a coin is flipped and lands on Heads, we can understand the problem in the context of probabilities.
First, let's define the random variable Z. In this case, Z can be defined as a function that assigns a value of 1 to the event of landing on Heads, and a value of 0 to the event of landing on Tails. So, Z takes on two possible values: 1 (when Heads) or 0 (when Tails).
We can represent the possible outcomes with a probability distribution. Since we are flipping a fair coin, the probabilities of landing on Heads and Tails are both 0.5 (or 50%). Hence, P(Z = 1) = 0.5 (probability of Heads) and P(Z = 0) = 0.5 (probability of Tails).
Now, the question is whether the value of Z will be greater than or equal to 0. Since the value 0 is included in the possible values Z can take (Z = 0 or Z = 1), the condition Z ≥ 0 is always true. In other words, there is no scenario in which Z would be less than 0.
Therefore, regardless of whether the coin lands on Heads or Tails, the value of the random variable Z will always be greater than or equal to 0.