Understanding Random Variables and Probability Distributions, Summaries of Mathematics

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RANDOMRANDOM

VARIABLEVARIABLE

Statistics and Probability Week 1

learning competencieslearning competencies

At the end of this session, the students are able to:

1. illustrate a random variable;

2. distinguish between a discrete and a continuous

random variable;

3. find the possible value of a random variable;

RANDOM VARIABLERANDOM VARIABLE

It is a variable (typically represented by X) that has a single numerical value, determined by chance, for each outcome of a procedure (Triola, 2018).

RANDOM VARIABLERANDOM VARIABLE

CONTINUOUS random variableCONTINUOUS random variable

It has infinitely many values, and the collection

of values is not countable (Triola, 2018)

DISCRETE random variableDISCRETE random variable

It is a collection of values that is finite or

countable (Triola, 2018)

RANDOM VARIABLERANDOM VARIABLE

6. U: The time needed to finish the test. 7. V: The amount of sugar in a cup of coffee. 8. W: The number of accidents per year at an intersection. 9. X: The average amount of electricity consumed per household per month. 10. Y: The number of deaths per year attributed to lung cancer. Instruction: Determine if the given statement is discrete or continuous.

RANDOM VARIABLERANDOM VARIABLE

6. U: The time needed to finish the test. 7. V: The amount of sugar in a cup of coffee. 8. W: The number of accidents per year at an intersection. 9. X: The average amount of electricity consumed per household per month. 10. Y: The number of deaths per year attributed to lung cancer. Instruction: Determine if the given statement is discrete or continuous.

EXAMPLE 2EXAMPLE 2

Three coins are tossed. Let "Z" be the random variable representing the number of heads that occurs. Find the values of the random variable "Z" with its corresponding probabilities.

EXAMPLE 3EXAMPLE 3

A shipment of five computers contains two that are

defective. If a retailer receives three of these

computers at random, list the elements of the sample

space S using the letters D and N for defective and

non-defective computers, respectively. To each

sample point, assign a probability value of the random

variable X representing the number of computers

purchased by the retailer which are defective.

EXAMPLE 4EXAMPLE 4

Two fair dice are thrown simultaneously. Let the random variable "X" as the sum of the two spots in throwing the two fair dice simultaneously and write its corresponding probabilities.

EXERCISE 2EXERCISE 2

Instruction: Determine whether the given table is probability distribution or not.

EXERCISE 3EXERCISE 3

The table below is a probability distribution of a discrete random variable X. Find the following probabilities.

LeARN MORELeARN MORE

How many ways you can choose 1 pen?

LeARN MORELeARN MORE

How many ways you can choose 2 pens?