5 Probability for Business Analytics Free Online FlashCards

How do experiment, outcome, and event differ?

An experiment is an uncertain process, an outcome is one possible result, and an event is a set of outcomes.

What is the complement rule?

The probability that event $A$ does not occur is $P(A^c)=1-P(A)$.

How do you find the probability of $A$ or $B$?

Add the probabilities of the two events, then subtract their overlap: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

What does conditional probability measure?

Conditional probability is the chance of $A$ given $B$: $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$, where $P(B)>0$.

When are two events independent?

They are independent when knowing that one occurred does not change the probability of the other; then $P(A\cap B)=P(A)P(B)$.

What is a random variable?

A random variable assigns a numerical value to each possible outcome of an uncertain process.

What does a discrete random variable’s PMF describe?

A discrete random variable takes countable values. Its probability mass function gives $P(X=x)$ for each value; the probabilities sum to $1$.

How do probabilities work for a continuous variable?

A continuous variable can take any value in a range. Probabilities are areas over intervals, and the probability of any exact single value is $0$.

What does the cumulative distribution function $F(x)$ give?

The cumulative distribution function is $F(x)=P(X\le x)$; it gives the probability that the variable is at most $x$.

How is the expected value of a discrete variable calculated?

For a discrete variable, $E(X)=\sum_x xP(X=x)$. It is the probability-weighted long-run average, not a guaranteed value for one observation.

How are variance and standard deviation related?

Variance measures spread around the expected value; standard deviation is its square root: $\sigma_X=\sqrt{\operatorname{Var}(X)}$.

What process does the binomial distribution model?

A binomial variable counts successes in a fixed number $n$ of independent trials with the same success probability $p$. Its mean is $np$, and its variance is $np(1-p)$.