C. Get the summation of the produc variable and its probability. D. Get the square root of the discrete random varial 4. What can we general What I Need to Know This module was created and written with you in mind on how to calculate the mean and variance of a discrete random variable. This will also help you analyze real-life situated problems statistically in terms of relevant questions for you to better understand them. Your adept at analysis will help you appreciate the richness, and beauty of Statistics which will motivate you to apply to similar events and create statistical measures of your own. From this module, you will also learn how to determine the value of the mean, variance, and standard deviation of the discrete random variables, and the purpose of the author for a better understanding of the story. Your patience in solving problems here in the module will help you upgrade your computational skills as it tackles appropriate culture-based situated problems. Your ability to explain, reason-out, and make a judgment or even decision out of statistical measures will also be practiced here. The extent of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using. The module focused on calculating the mean and variance of a discrete random variable. After going through this module, you are expected to: 1. apply the important concepts of mean and variance of a discrete random variable; and 2. calculate the mean and variance of a discrete random variable. What I Know Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. 1. Which of the following is NOT included in the process of calculating the mean of the discrete random variable X? A. Identify the correct probabilities for each x value. B. Multiply each x value by its probability. C. Get the summation of the product. D. Get the square root of the product. 2. Which of the following is TRUE about the value of the mean of a discrete random variable? A. Mean Value is always equal to 1 B. Mean Value cannot be negative. C. Men value is equal to the expected value D. Mean, Variance, and Standard Deviation are equal. 3. To determine the expected value of the discrete random variable which processes should be done? A. Get the squared sum of the difference of each value of a discrete random variable its probability. B. Get the summation of the difference of each value of a discrete random variable and its probability.to calculate the mean analyze real-life to better and C. Get the summation of the product of each value of a discrete random variable and its probability. D. Get the square root of the summation of the product each value of a discrete random variable and its probability. 4. What can we generate if we take the squares of standard deviation? A. Expected Value B. Mean Value C. Probability value D. Variance A. 0 5. In tossing a coin, what are the possible values of the random variable X? B. 0, 1 6. If the variance of a probability distribution is 2.6 grams, what is the standard C. 1 , 2 D. 0, 1, 2 deviation? A. 1.61 B. 1.16 C. 1.06 D. 1.01 For items 7-10, refer to the scenario provided below. Juan is not a very smart student. When he tries to answer a multiple-choice question, he used to guess everything. Suppose, he is taking a quiz that has two multiple choice questions on it and that each question has four possible answers only one of which is correct. Let X represent the number of correct answers on the quiz. 7. What are the possible values of the random variable X? A. 0 B. 0 , 1 C. 1, 2 D. 0, 1, 2 8. Which probability distribution is an appropriate presentation of the given scenario? A. X 0 2, P(X) 0.5625 0.375 0.0625 B. 0 2 P(X) 0.0625 0.5625 0.375 C. X 2 P(X) 0.375 0.0625 0.0625 D. X 0 2 P(X) 0.5625 0.0625 0.375 9. What is the expected value of the discrete probability distribution? A. 0.5 B. 0.4 C. 0.05 D. 0.04 10. What is the probability that Juan gets at least 1 correct answer? A. 0.0625 B. 0.375 C. 0.4375 D. 0.5625 For items 11-12, refer to the scenario and table provided below. In a recent Barangay Basketball League, each player went to free throws 2 times The number of free throws made by each player is described by the following probability distribution. Number of free throws, Probability, P(X) X O 0.20 1 0.45Figure B Figure A 6 00 10 3 4 9 Figure C A. Compare the means of the three figures. B. Show the relationship between the variance and standard deviation among three given figures.Figure B P(X) 0.5 COVID-19 Patients 0.4 0.2 0. 1 0 16 X 17 18 19 1. Find the probability that in a given hour: a. exactly 17 patients arrive; b. at least 16 patients arrive; and c. at most 18 patients arrive. 2. What is the average number of COVID-19 patients who arrived in the ER in an hour? 3. Illustrate the mean and standard deviation of the data gathered. Solution: 1, a. P(X = 17) = 0.20 b. P (X 2 16) = 0.2 + 0.2 + 0.1 + 0.1) = 0.6 C. P(X = 18) = 0.4 + 0.2 + 0.2 + 0.1) = 0.9 2. Hx= 17 3. It shows the hat element spread 3 away from the mean which implies its variability P(X) 0.45 15 0.4 0.35 0.3 0.25 0.2 0.15 0.05 ON 0.35 1 1. What is the mean of the probability distribution? A. 1.00 B. 1.15 C. 2.00 D. 2.25 12. What is the probability that both free throws will be out of the basket? A. 0.20 B. 0.45 C. 0.35 D. 1.00 For items 13-15, refer to the scenario and table provided below The number of qualified voters living in the household on a randomly selected Subdivision block is described by the following probability distribution. Number of qualified voter/s, x Probability, P(X) 0.25 0.50 0.15 0.10 13. What is the mean of the probability distribution? A. 1.0 B. 1.8 C. 2.0 D. 2. 1 14. What are the variance and standard deviation respectively of the probability distribution? A. 0.99 and 0.50 B. 0.89 and 0.62 C. 0.79 and 0.89 D. 0.80 and .088 15. What is the probability that less than 3 votes will be in any household? A. 0.25 B. 0.50 C. 0.75 D. 1.00 Lesson 1 Calculating Mean and Variance of Discrete Random Variablevariance is in cm ton is in centimeter (cm), while the Remember that with respect on units: 1. o has the same units as X. 2. Var(X) has the same units as the square of X. So, if X is in meters, then. Var(X) is in meters squared. Because o and X have the same units, the standard deviation is a natural measure of spread. Always remember that the variance cannot be negative, because it is an average of squared quantities. This is appropriate, as a negative spread for distribution does not make sense. Hence, 6 , 20 and 5x (X) 20. What's More Independent Activity 1: Study and analyze The number of shoes sold per day at a retail store is shown in the table below. Illustrate the mean, variance, and standard deviation of this distribution. X 19 20 21 22 23 PIX 0.4 0.2 0.2 0.1 0.1For items 12-15, refer to the scenario an In her Flower Shop, Vera recorded the flower arrangements that she de Independent Assessment 1: Fill me in and solve Write all the necessary formula and show the complete solution. Formula to be used: a. Mean b. Variance_ Solution: c. Standard Deviation Independent Activity 2: Study and analyze The number of patients seen in the Emergency Room in any given hour is a random variable represented by x. The probability distribution for x is: X 10 11 12 13 14 P(X) |0.4 0.2 0.2 0.1 0.1 Independent Assessment 2: Fill me in and solve Write all the necessary formula and show the complete solution. Formula to be used: a. Mean b. Variance c. Standard Deviation Solution: Independent Activity 3: Study and analyze Suppose that a coin is to be tossed four times, and let X represent "the number of TAILS that can come up". Find the mean, variance, and standard deviation of this distribution. X 2 3 4 P(X) 4 6 16 16 4. 16 8 16 16 Independent Assessment 3: Fill me in and solve Write all the necessary formula and show the complete solution. Formula to be used: a. Mean b. Variance c. Standard Deviation_ Solution: What I Have Learned 1. The formula for calculating Mean or Expected value is of 2. I have discovered that the Expected Value E(X) is only the because more random variable X. It's occasionally called a frequent values of X are weighted more highly in the average. 3. The variance of a discrete random variable X is defined The standard deviation of X is defined to be the square root of the variance of 4 . X. In symbol it expressed into1.5819 J ( x -4 ) 2 . P(X ) 5 . The variance cannot be quantities. Hence, of x 2 0 and ox (X) 20. What I can do because it is an average of squared LET'S DO FAMILY PLANNINGI Things to do: 1. Create a short script as if you are with your dream partner in life and you both talking about Family Planning 2. During your planning, specify in your decision how many girls (G) and boys X stand for. (B) in the family you both want to have. Consider also your random variable you had. 3. After your planning, construct a probability distribution of whatever decision 4. Based on the probability distribution table, illustrates the following: a. Mean or Expected Value; b. Variance; and c. Standard Deviation. . Share your output to the Class Group Chat through Image or Video Presentation. TASK CRITERIA Accuracy of the solution 50% Clarity and content of the script 25% Originality and creativity of the 25% Presentation TOTAL 100% Assessment Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. 1. What formula is appropriate to use in calculating the expected value? A. E(x) = Ex -P (x) B. E(x) = Ex-P(x) C. E(x) = Ex . p (x) D. E(x) = Ex/P (x) 2. Which among the list of formulas should be used to solve for the variance of discrete random variables of the given data above? A. ox = [(x + ()2 . P(x); for all possible values of x B. ox = [(x - u)2 . P(x); for all possible values of x C. of = Ex . P(x); for all possible values of x D. of = [(P(x) + M)2 . x; for all possible values of x 3. Which of the following statements does not describes the value of the standard deviation? A. A small standard deviation (or variance) means that the distribution of the random variable is narrowly concentrated around the mean.For items 12-15, refer to the scenario and table provided below. In her Flower Shop, Vera recorded the probability distribution for the number of flower arrangements that she delivered each day. 00 P(X) 10.20 10 11 0.20 0.30 0.20 10.10 12. What is the probability that she made at least 9 flower arrangements? A. 0.60 B. 0.50 C. 0.40 D. 0.30 13. What is the mean or expected value of the given probability distribution? A. 8.5 B. 8.6 C. 8.7 D. 8.8 14. Which of the following is the appropriate value for the variance? A. 1.55 B. 1.56 C. 1.57 D. 1.58 15. What value corresponds to the standard deviation? A. 1.25 B. 1.26 C. 1.27 D. 1.28 Additional Activities 1. Willie works in an automotive tire factory. The number X of sound but blemished tires that he produces on a random day has the probability distribution P(X) 0.48 0.35 0.10 0.07 a. Find the probability that Leomar will produce more than three blemished tires. b. Find the probability that Leomar will produce at most four blemished tires. c. Calculate the mean, variance, and standard deviation of a discrete random variable. 2. The Land Bank of the Philippines Manager claimed that each saving account customer has several credit cards. The following distribution showing the number of credits cards people own. 0.08 0.03 0.44 P(X) 0.18 Show the complete table of values in calculating the Mean, Variance, and Standard Deviation.B. A large value of standard deviation (or variance) indicates that the distribution is spread out, with some chance of observing values at some distance from the mean. variance. C. Standard deviation is obtained by getting the square root of the D. It is obtained by squaring the variance. 4. What can we generate if we take the summation of the product of each value assigned to the random variable and its corresponding probability? A. Expected Value B. Probability value C. Standard Deviation D. Variance 5. Suppose that a coin is to be tossed four times, and let X represent "the number of TAILS that can come up", what are the possible values of the random variable X? A. O B. 0, 1 C. 1 , 2,3 D. 0, 1, 2 , 3, 4 6. Which of the following is the correct value of standard deviation (o) of a discrete random variable X if the variance is 2.5754? A. 1.61 B. 1.60 C. 1.06 D. 1.01 For items 7-9, refer to the scenario and table provided below. Let X be a random variable defining number of students getting 95 above grade. P(X) 0.2 0.4 0.3 7. What is the expected value of X from the given table? A. 1.3 B. 1.8 C. 1.9 D. 2.3 8. What is the variance (ox) of the given probability distribution? A. 1.16 B. 1.18 C. 1.20 D. 1.28 9. Which of the following value is appropriate for deviation (x) of the given probability distribution? A 1.02 B. 1.04 C. 1.06 D. 1.08 10. A Grade 11 - HUMMS researcher surveyed the households in Brey. Quipot, Tiaong Quezon. The random variable X represents the number of college graduates in the households. The probability distribution of X is shown below. P(X) 0.25 0.25 Find the values of variance and standard deviation. A. 0.3 and 0.51 respectively B. 0.4 and 0.61 respectively C. 0.5 and 0.71 respectively D. 0.6 and 0.81 respectively 1 1. In the 50 items test, Miss Santos, a Mathematics teacher claimed that most of the students' scores lie closer to 40. In this situation, which of the following terms parallel to the score of 40? A. Variance B. Standard Deviation C. Expected Value or Mean D. Median