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Definition

Definition A random variable is a variable whose value is determined by the outcome of a random experiment/chance situation. Discrete Random Variable. Definition A random variable that assumes isolated, separated values is called a discrete random variable . THINK : Counts!!!.

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Definition

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  1. Definition • A random variable is a variable whose value is determined by the outcome of a random experiment/chance situation.

  2. Discrete Random Variable • Definition • A random variable that assumes isolated, separated values is called a discrete random variable. THINK : Counts!!!

  3. Examples of discrete random variables • number of cars sold at a dealership during a given month • number of houses in a certain block • number of fish caught on a fishing trip • number of complaints received at the office of airline on a given day • number of customers who visit a bank during any given hour • number of heads obtained in three tosses of a coin

  4. Continuous Random Variable • Definition • A random variable that can assume any value contained in an interval is called a continuous random variable.

  5. Examples of continuous random variables • The height of a person • The time taken to complete an examination • The amount of milk in a gallon (note that we do not expect a gallon to contain exactly one gallon of milk but either slightly more or slightly less than a gallon.) • The weight of a fish

  6. PROBABLITY DISTRIBUTION OF A DISCRETE RANDOM VARIABLE • Definition • The probability distribution of a discrete random variable lists all the possible values that the random variable can assume and their corresponding probabilities.

  7. Two Characteristics of a Probability Distribution • The probability distribution of a discrete random variable possesses the following two characteristics. • 0 ≤ p (x) ≤ 1 for each value of x • Σp(x) = 1

  8. Class Examples …

  9. MEAN OF A DISCRETE RANDOM VARIABLE The mean of a discrete variablex is the value that is expected to occur per repetition, on average, if an experiment is repeated a large number of times. It is denoted by µ and calculated as µ = Σx P (x) The mean of a discrete random variable x is also called its expected value and is denoted by E (x); that is, E (x) = Σx P (x)

  10. STANDARD DEVIATION OF A DISCRETE RANDOM VARIABLE • The standard deviation of a discrete random variablex measures the spread of its probability distribution and is computed as • Note: variance

  11. Class Examples …

  12. The Binomial Experiment Conditions of a Binomial Experiment A binomial experiment must satisfy the following four conditions. • There are n identical trials. • Each trail has only two possible outcomes. • Probabilities of the two outcomes constant. • The trials are independent.

  13. The Binomial Probability Distribution and Binomial Formula • For a binomial experiment, the probability of exactly x successes in n trials is given by the binomial formula • also Binomial Tables & Software!! • Where n = total number of trials • p = probability of success • 1 – p = probability of failure (= q) • x = number of successes in n trials • n - x = number of failures in n trials

  14. Mean and Standard Deviation of the Binomial Distribution • The mean and standard deviation of a binomial distribution are • where n is the total number of trails, p is the probability of success, and q is the probability of failure.

  15. Class Examples …

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