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- following random 2. Let W be a random variable giving 1. Classify variables as discrete or continuous a. X: the number of automobile accidents per year in EDSA b. Y: the length of time to paly 18 holes of golf. c. M: the amount of eggs laid each month by a hen. d.P: the number of building permits issued each month in Camiling, the the number of heads minus the number of tails in three tosses of a coin. a. List all elements of the sample space S for the three tosses of the coin and to each sample point assign a value w of W. b. Find the probability distribution of the random variable W, assuming that the coin is biased so that a head is twice as likely Tarlac e. Q: the weight of grain produces per hectare. to occur as a tail. c. Compute for value, variance and standard deviation variabe W. the expected of the randomAnswer the following questions on a separate sheet of paper. 1. Determine if each of the following situations illustrates a continuous random variable or not. weight of a randomly selected grade 11 student a. b. number of Filipino people who will vote in the next national election fastest speed of a randomly selected car racer in a car racing competition С. d. a farmer's record of the number of mongo seeds in a sack.1 The highest score in a game of dice (a) A random variable X is defined as the larger of the scores obtained in two throws of an unbiased, six-sided, die. Show that (2x - 1) Pr(X x) = x = 1, 2, . .., 6. %3D 36 (b) A random variable Y is defined as the highest score obtained in k independent throws of an unbiased, six-sided, die. Find an expression for the probability function of Y.
- Answer the following questions. 1. The amount of rainfall in California in 2021 is A) A discrete random variable B) A continuous random variable C) Not a random variable 2. The amount of rainfall in California in 2019 is A. A discrete random variable B. A continuous random variable C. Not a random variable 3. The number of tesla cars sold in 2020 in the us is A. A discrete random variable B. A continuous random variable C. Not a random variable 4. The most popular car maker (i.e., the car maker that sold the most cars) in the us in 2021 is A. A discrete random variable B. A continuous random variable C. Not a random variableA. Classify each random variable as discrete or continuous. 1. X: Number of women among 20 newly hired teachers 2. Y: Height (in centimeters) of a 30 randomly selected adult males 3. Z: Number of car accidents among 8 selected cities 4. A: Amount of rainfall (in millimeters) in different cities in Metro Manila 5. B: Number of gifts received by 20 students during Christmas seasonb. Let X1, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means H1 = 3.6, 42=0.9, 3= 1.8, 4 = 7.4 pounds and variances o = = = Find P (2X₁ + 1X2 + 3X3 + 1X4 ≤ 17.6). = 1.
- Aa.127. Let X1,X2,...,X4 be indepedent Poisson random variables with rates λ1,...,λ4, respectively. Show that X1 + X2 + X3 + X4 is a Poisson random variable with rate λ1 + λ2 + λ3 + λ4.1. Identify if the following scenarios describe a discrete or continuous random variable. Explain your choice. (a) X = The number of persons in an emergency room 181screte (b) W = The weights of delivery trucks at a supermarket. Lconinaas (c) H= The areas of houses being built in a new subdivision. 2. Faith is a 95% free throw shooter. At practice, each player shoots 20 free throws. L X the number of free throws Faith makes out of 20 shots. (a) Explain why X is a binomial random variable. (b) Calculate the mean of X. (c) Calculate the standard deviation of X. (d) Use the binomial probability formula to find P(X = 19). Interpret this value in context. (e) Her coach says that he will let the team out of practice early if Faith makes 18 or me free throws. What is the probability that practice ends early? Show your work. 2017 BFW Publishers Starnes/Tabor Statistics and Probability with Applications 3/eA continuous random variable X has cumulative distribution function F(x) = 1 – e-0.8z, x > 0. a) Find the density function of X. f(x) z >0 b) Find the probability that X 3. d) Find the probability that X = 5.