Final answer:
Brenoulli random variables pertain to experiments with two possible outcomes classed as success or failure, with constant probabilities and independent trials, such as tossing a fair coin, checking a light switch, or monitoring a server's status.
Step-by-step explanation:
Bernoulli random variables are associated with experiments that have exactly two possible outcomes, which are classified as either a success or a failure. These variables are cornerstone concepts in probability theory and can apply to various situations.
- Tossing a fair coin and recording whether it lands heads or tails is a fundamental example of a Bernoulli random variable where the probability of success (heads) is 0.5 and the probability of failure (tails) is also 0.5.
- Checking a light switch to see if it is on (success) or off (failure) is another instance, assuming the light bulb is known to be functioning and each flip of the switch is independent of previous flips.
- A system that monitors whether a single server is up (success) or down (failure) at a given moment, considering each check is independent of others, also produces Bernoulli random variables.
Each of these scenarios fits the criteria for a Bernoulli trial, where the outcomes are binary, the probabilities of success and failure are constant, and each trial is independent of others.