Random Variables PDF

RANDOM VARIABLE Tossing a Coin Directions: Perform the experiment below. After performing, try to answer the questions that follows. If you are going to observe on the characteristics of the coin. One side contains a head, and we will represent that as H, while the other side which is the tail or...

RANDOM VARIABLE Tossing a Coin Directions: Perform the experiment below. After performing, try to answer the questions that follows. If you are going to observe on the characteristics of the coin. One side contains a head, and we will represent that as H, while the other side which is the tail or T. Steps: 1. Prepare 3 coins for the activity. 2. Toss the first coin then the second coin and followed by the last coin. 3. Record the result by writing and indicating whether it is H or T. If the results of your three tosses for example is heads, tails, heads, then you will write on the outcome HTH on the given table below. (Note: If the outcome is already repeated, do not write anymore the result. The outcomes should be unique.) 4. After recording, you will notice that there are only 8 possible outcomes and no matter how you will repeat the tossing, the result will always be one of the 8 outcomes you already had. 5. After writing all the possible outcomes, try to fill the given table below:  Experiments are any movement or activity which can be done repeatedly under similar or comparative condition. Outcomes are the result of a given experiment Sample space is the set of all possible outcomes of an experiment. Example : Upon rolling the die, it is expected that it will show a dot on the top which are either 1, 2, 3, 4, 5 or 6, these are what we call the sample space of the given experiment. If you are only interested on a given value of dots, let say, three dots, then “3” is what we call the outcome or the sample.  If there are 4 coins instead of three coins tossed, what number or value can be assigned for the frequency of heads that will occur? If three cards are drawn from a deck of card, what number can be assigned for the frequency of face cards that will occur? The answer to these questions requires a knowledge of random variable.  Variable - a characteristic or attribute that can assume different values (e.g. in algebra, variables like x can be any number). - use capital letter (X, Y, Z, and others) to denote or represent a variable. Random Variable A capacity that connects a real number with every component in the sample space. 0, 1, 2, 3 are Random Variable Sample Space / Possible Random Variable X Outcomes (number of boys in the family) BB 2 BG 1 GB 1 GG 0 Example 3: DEFECTIVE or NON-DEFECTIVE Suppose 4 laptops are tested at random. Let N represent the non-defective laptops and let D represent the defective laptops. If we let Z be the random variable for the number of non- defective laptops, determine the value of the random variable Z. Solution: Based on the given problem, there are 4 laptops that we will be tested at random and each laptop can either be defective or non-defective. Let us first determine the number of sample space. Since there are 4 laptops and each laptop can be defective or non-defective, then n(s) = (2)(2) (2) (2) =2^4 =16 sample space / possible outcomes. * Activity 1: FINDING MY VALUE! Directions: Find the possible values of the given random variable of the following experiments below. Write your answer on the space provided. 1. Supposed two coins are tossed, let P be the random variable representing the number of heads that occur. Find the values of the random variable P. Answer: The values of the random variable P are ________________. 2. Inside the box are 2 balls – one white and one yellow. Two balls are picked one at a time with replacement (meaning the ball is replaced once picked). Let X be the random variable representing the number of white balls. Find the values of the random variable X. TYPES OF RANDOM VARIABLE 1.Discrete Random Variables are variables that can take on a finite number of distinct values. In easier definition, discrete random variable is a set of possible outcomes that is countable. Examples :  the number of heads acquired while flipping a coin three times  the number of defective chairs  the number of boys in the family  the number of students present in the online class 2. Continuous Random Variable are random variables that take an infinitely uncountable number of potential values, regularly measurable amounts. Often, continuous random variables represent measured data, such as height, weights, and temperature. Experiment Random Variable X Types of Random Variable Types of Random The number of Discrete Variable defective phones. (Reason: You can count the number of defective phones) Buying two trays of The weight of eggs in Continuous eggs in the market kilograms. (Reason: Since we are talking about the weight of the eggs, and weight ismeasurable) Rolling a pair of The sum of the number Discrete dice. of dots on the top (Reason: Since the number of faces. dotsiscountable, it takes a finite number: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and12) Vehicular Accidents The number of Discrete happened in La accidents happened at (Reason: Accidents are countable) Union the intersection Learners will The time spent by the Continuous prepare for a quiz in learners studying for a (Reason: Time is a measurable unit) Mathematics quiz in Mathematics Activity 2: CLASSIFY ME! Directions: Classify whether the following random variables are DISCRETE or CONTINUOUS. Write D or C only. Write your answer on the space provided. ____1. The number of deaths per year attributed to lung cancer. ____2. The average amount of electricity consumed per household per month. ____3. The number of patient arrivals per hour at a medical clinic. ____4. The number of bushels of mangoes per hectare this year. ____5. The number of voters favoring a candidate. ____6. The number of people who are playing LOTTO each day. ____7. The amount of sugar in a cup of coffee. ____8. The time needed to finish the test. ____9. The number of female athletes in R1AA. ____10. The speed of a car. Activity #3 (10 pts.) Read the problem below. After reading, prepare a table just like what we did in the different examples previously. Problem: Four coins are tossed. Let G be the random variable representing the number of tail (T) that occur. Find the values of the random variable G. What to find: 1. The number of possible outcomes or sample space (S). 2. The sample spaces (place in the table). 3. The correct values of random variable G. 4. Interpretation or description about the value of the random variable G.