Random variable - created from Mind Map

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Quantity whose future outcomes are uncertain

Discrete

Continuous

Associated with a probability distribution that describes the variable completely

can take on at most a countable number of possible values.

Probability Distribution

The Discrete Uniform Distribution

The Binomial Distribution

The distribution has a finite number of specified outcomes, and each outcome is equally likely.

When we make probability statements about a record of successes and failures, or about anything with binary outcomes

Bernoulli random variable

we cannot count the outcomes

Probability Distribution

Continuous Uniform Distribution

The Normal Distribution

Lognormal Distribution

describes equally likely outcomes

The normal distribution is completely described by two parameters—its mean, μ, and variance, σ2.

Aplications

mean–variance analysis

Stress testing/scenario analysis

Value at Risk

used for modeling the probability distribution of share and other asset prices.

Probability function

Probability density function

specifies the probability that the random variable takes on a specific value: P(X = x) is the probability that a random variable X takes on the value x.