Module 1. RANDOM VARIABLES & PROBABILITY DISTRIBUTION WRITTEN OUTPUT A. Classify the following random variables as discrete or continuous. __________ 1. The weight of the newborn in a hospital __________ 2. Length of wire ropes __________ 3. Number of soldiers in a troop __________ 4. Amount of gasoline fuel consumed by a car in a day __________ 5. Number of winners in lotto for the week __________ 6. Number of ants in a colony __________ 7. The number of patients a doctor sees in a day __________ 8. Student’s grade level __________ 9. The speed of a motor vehicle __________ 10. Body temperature of a COVID-19 patient B. COMPLETE the table below as indicated. Two balls are drawn in succession without replacement from an urn containing 5 orange balls and 6 violet balls. Let V be the random variable representing the number of violet balls. Steps Solution 1. List the sample space 2. Count the number of violet balls in each outcome and assign this number to this outcome 3. Construct the frequency distribution of the values of the random variable V. 4. Construct the probability distribution of the random variable, V Possible Outcome Value of the Random Variable, V Number of Violet Balls, V Number of Occurrence (Frequency) Number of Violet Balls, V Number of Occurrence (Frequency) Probability P(V) 5. Construct the probability histogram. (Use another sheet, if possible) C. Which of the following shows a discrete probability distribution? Explain why. 1. 2. 3. 4. 5. Let X be a random variable with the following probability distribution: 6. Find P(X=3). 7. Find P(Y=1). MEAN & VARIANCE A. Determine the Mean or Expected Value of random variable below. X 1 2 3 4 P(X) 2 15 4 15 8 15 1 15 X ∙ P(X) ∑ X ∙ P(X) = _____________ B. The number of cars sold per day at a car center with its corresponding probabilities is shown in the table below. Using 𝜇 = 5, complete the table. ∑(X − μ)2 𝑃(𝑥) = _______________ C. Compute for the variance and standard deviation of the Probability Distribution Table of the Random Variable X in the given above. A. Variance = 5; Standard Deviation = 2.24 B. Variance = 4; Standard Deviation = 3.24 C. Variance = 3; Standard Deviation = 4.24 D. Variance = 2; Standard Deviation = 5.24 PERFORMANCE TASK Using your Facebook account, conduct a survey on the number of online activities your friends and classmates are involved in. Construct a probability distribution and compute the mean, variance and standard deviation. Interpret the result.