Question

List the conditions for a function to be a random variable?
Define sample space and classify the types of sample space.
Define Joint and Conditional Probability.
Define Equally likely events, Exhaustive events and Mutually exclusive events.

Answer 1

Answer:

In the development of the probability function for a discrete random variable, two conditions must be satisfied:

(1) f(x) must be nonnegative for each value of the random variable, and

(2) the sum of the probabilities for each value of the random variable must equal one.

In probability, sample space is a set of all possible outcomes of an experiment.

1. A sample space can be finite or infinite.
2. A sample space can be discrete or continuous.
3. A sample space can be countable or uncountable.

Joint probability is the probability of two events occurring simultaneously. Marginal probability is the probability of an event irrespective of the outcome of another variable.

Conditional probability is the probability of one event occurring in the presence of a second event.

Equally likely events are events that have the same theoretical probability (or likelihood) of occurring. Example. Each numeral on a die is equally likely to occur when the die is tossed. Sample space of throwing a die: { 1, 2, 3, 4, 5, 6 }

In probability theory and logic, a set of events is jointly or collectively exhaustive if at least one of the events must occur. The set of all possible die rolls is both mutually exclusive and collectively exhaustive (i.e., "MECE"). The events 1 and 6 are mutually exclusive but not collectively exhaustive.

In logic and probability theory, two events (or propositions) are mutually exclusive or disjoint if they cannot both occur at the same time. A clear example is the set of outcomes of a single coin toss, which can result in either heads or tails, but not both.