The correct answer is True.
A Bernoulli random variable is a random variable that takes on only two values, usually denoted as 0 and 1. The value 1 is often interpreted as “success” and the value 0 as “failure”.
For example, if you flip a coin, the outcome is a Bernoulli random variable. The possible values are 0 (heads) and 1 (tails).
Another example is a coin toss with a biased coin. If the probability of heads is 0.6, then the outcome of the coin toss is a Bernoulli random variable with probability 0.6 of being 1 (heads) and probability 0.4 of being 0 (tails).
Bernoulli random variables are often used in probability and statistics. For example, they can be used to model the probability of success in a trial. They can also be used to model the probability of a certain event occurring.
Here is a brief explanation of each option:
- A. True. Bernoulli random variables take (only) the values 1 and 0.
- B. False. Bernoulli random variables can take on any value between 0 and 1.
I hope this helps! Let me know if you have any other questions.