Random Variables - Statistics & Probability - SY 2024-2025 PDF

Statistics and Probability  Statistics and Probability Statistics and Probability is a core subject which is taken by the Grade 11 students of the Senior High School across all STRANDS. It is also an essential part of your Research Subject and Paper. ...

Statistics and Probability  Statistics and Probability Statistics and Probability is a core subject which is taken by the Grade 11 students of the Senior High School across all STRANDS. It is also an essential part of your Research Subject and Paper.  What is Statistics? Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. According to Merriam-Webster dictionary, statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”. According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”.  What is Probability? Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. Let us have this activity!  RANDOM VARIABLES AND PROBABILITY DISTRIBUTION September 1 - 5, 2024 Ms. Arlene A. Aboga, MEd OBJECTIVES OF THE LESSON:  RANDOM VARIABLES  WHAT IS A RANDOM VARIABLE? 1) A set of possible values from a random experiment 2) It may be viewed as a way to map outcomes of statistical experiments determine by chance into a number. 3) It is denoted by a capital letter, usually X 4) Alternatively, the value of a random variable can be either numerical or  RANDOM VARIABLES DISCRETE CONTINU OUS  BRAINSTORM Which of the following are Discrete or Continuous? A = the sum of the numbers that turn up when a pair of dice is tossed. B = the distance leaped in meters by a long - jumper W = theinlength a competition. of time in minutes that a scheduled airplane flight is of X = the number delayed. correct answers a student get in a 10-item multiple choice test. Y = the length of time it takes a swimmer to complete a 200 - meter freestyle race. Z = the number of defective bulbs in a sample of 10 randomly selected bulbs from a manufacturing company.  RANDOM DISCRETE CONTINUOUS VARIABLES A = the sum of the numbers that turn up B = the distance leaped in meters by a long - when a pair of dice is X = the number of correct jumper in a competition. tossed. W = the length of time in answers a student get in a minutes that a scheduled 10-item multiple choice airplane flight is delayed. test. Z = the number of Y = the length of time it defective bulbs in a takes a swimmer to sample of 10 randomly complete a 200 - meter selected bulbs from a freestyle race.  RANDOM VARIABLES DISCRETE When it can take on a finite number of When a random distinct values. variable can take only When it is mostly countable values, or its whole numbers. set of possible values is in one-to-one correspondence with a  RANDOM VARIABLES CONTINU Typically measurable quantities. OUS When a random variable takes an The value given to an observation can uncountable infinite number of values as a include values as When its set of result of measurement. small as the possible values is from instrument of a range of real measurement allows.  Classify if the following is discrete or continuous: 1) Number of eggs DISCRE in 2) aThe basket. number of votes in TE DISCRE an election. 3) Water temperature. TE CONTINU 4) Number of diaper OUS DISCRETE changes in a day. 5) The speed of the wind. CONTINU OUS BOOK ACTIVITY  POSSIBLE VALUES OF A RANDOM Values that are obtained from functions VARIABLE that assign a real number to each point of a sample space. Example: If a basketball team will play for three consecutive games, the sample space is the set of all possible outcomes of the events. Let’s say W stands for a win and L stands for a loss. What are the possible sample {WWW, WWL, WLW, WLL, LWW, LWL, space of the results of the 3 consecutive games? LLW, LLL} We can assign numeric values to these outcomes as {1, 2, 3, 4, 5, 6, 7, 8}. Thus, there are 8 possible outcomes of 8 Suppose two coins are tossed. Let X be the random variable representing the number of tails that occur. Find the value of the random variable X. Value of the Possible random variable Outcomes X (number of tails) H 0 H H 1 T T 1 H T 2  HEADS OR TAILS? Choose 'heads' or tails'. Flip a coin 3 times and record the data below. Repeat Tally the the same experiment information then Graph compare the data and discuss the results: Heads Tails Heads Tails QUESTIONS Discuss your results with your seatmate. Were your results the same? Why / why not? How were they different? Why were they different?  ROLL A DIE The number that turn up in tossing a die. Possibl e Outco 1 2 3 4 5 6 mes Value 1 2 3 4 5 6 of Z  POSSIBLE VALUES OF A RANDOM VARIABLE Event: NUMBER Value of the random Possible variable X OF WINS (which Outcomes (number of is now our wins) random variable) WWW 3 WWL 2 X= WLW 2 LWW 2 WLL 1 LWL 1 LLW 1 We can show the probability of any one value using this style: P(X = value) = probability of that value Example (continued): Throw a die once X = {1, 2, 3, 4, 5, 6} In this case they are all equally likely, so the probability of any one is 1/6 P(X = 1) = 1/6 P(X = 2) = 1/6 P(X = 3) = 1/6 P(X = 4) = 1/6 P(X = 5) = 1/6 P(X = 6) = 1/6 Note that the sum of the probabilities = 1, as it should be.  Value of the Possible random variable Outcomes X (number of tails) HH 0 HT 1 TH 1 TT 2 X = {0, 1, 2} WRITE THE POSSIBLE VALUES OF EACH RANDOM VARIABLE. X = number of heads in tossing a coin thrice. Y = dropout rate (%) in a certain high school. Z = number of women among 10 newly hired teachers. A = number of odd number outcomes in a roll of a die WRITE THE POSSIBLE VALUES OF EACH RANDOM VARIABLE. SEATWORK: WRITE THE POSSIBLE VALUES OF EACH RANDOM VARIABLE. 1) X: Number of even outcomes in a roll of die. 2) Y: Weight (in mg) of a powder that does not exceed 80 mg. 3) Z: Number of heads in 4 flips of a coin. 4) A: Length (in cm) of a shoelace that is not longer than 2 meters. 5) B: Scores of a student in a 10-item test. What chance is there of getting a purple gumball? What chance is there of getting a yellow gumball? How likely is it you will get a purple gumball? What chance is there of getting a purple gumball? What chance is there of getting a yellow gumball? How likely is it you will get a yellow gumball? QUESTION TIME