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Solves problems involving mean and the variance of probability distribution. Two balls are drawn in succession without replacement from a box containing 5 red balls and 6 blue balls. Let x be the random variable representing the number of blue balls. Find the values of the random variable x. construct a probability distribution and compute the mean, variance and standard deviation. Solution: a. Determine the sample space. Let B represent the blue ball and R represent the red ball. The sample space for this experiment is: 5 = {RR, RB, BR, BB} | Possible Outcomes Count the number of blue balls in each outcome in the sample space and assign this number to this outcome. = \"RR the possible values of the random variable x are 0, 1, and 2. BE Construct the probability distribution representing th number of blue balls. Construct a probability distribution and BB compute the mean, variance and standard deviation. Note that the sum of F (r ) must equal to 1. T T 2P ix j=l fe=ex 'Po& js 1 o =i ~) Pe j= 0.707107 = 0.71 Interpretation: Therefore, the mean, variance and standard deviation of the random variable representing the number of blue balls occur are 1, 0.50 and 0.71 respectively. F. ACTIVITIES: Directions: Answer the following activities. Write your answer in your activity notebook. Note: Do not forget to write your name in your activity notebook. 1. Interprets the mean and the variance of a discrete random variable The probabilities that a doctor will operate 1, 2, 3, or 4 COVID-19 patients are 0.45, 0.30, 0.15 and 0.10, respectively. Compute the mean, variance and standard deviation. Interpret the result. x Po) 2. Solves problems involving mean and the variance of probability distribution. A basket contains 10 red balls and 4 white balls. If three balls are taken from the basket one after the other. Let R representing the number of red balls. 0.30 0.15 a.Determine the sample space b.Find the values of the random variable x c.Construct a probability distribution and compute the mean, variance, and standard deviation. dinterpret the result. G. REFERENCES: (DepEd-BLR), Department of Education-Bureau of Learning Resources. LAS (DepEd-Sarangani), LAS Writer: Corinne Ann M. Formoso