m(t) = 2e', defined for t e IR.
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Find the pmfs corresponding to the following mgfs defined for a discrete random variable. Write your solutions in the form
for a set Y to be identified, or identify the distribution by name with any parameters identified. If the
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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 sackb. 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.
- Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?Assume the flying height of an airplane is a Gaussian Random variable X with ax = 5000 m and ox=2000 m. Find the probability of the airplane flying higher than 10000 m. Use the table method.Q7 Fast and correct
- A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following (refer Table 4): Employees y X1 X2 1 100 9 6 2 90 4 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 2 4 8 30 2 2 (a) Run a regression analysis based on the data in Table 4 using Mic. Office EXCEL. Based on theoutput, propose a regression equation that can be used to predict paralegal GPA.(b) Interpret the coefficient value of each independent variable in the constructedmodel(c) Is each independent variable sharing a significant linear relationship with the dependent variable?Verify at 0.05 level of significance. Make your conclusion based on the p-value in the EXCEL output.A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.Q.2 Listed is a series of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whether the random variable is discrete or continuous. ilitu distrib blo llowe
- Soledad and Tania are both high school students. The number of texts Soledad sends daily, S, is approximately Normally distributed with a mean of 100 and a standard deviation of 6 texts. The number of texts Tania sends daily, T, is approximately Normally distributed with a mean of 108 and a standard deviation of 8.1 texts. Assume that S and T are independent random variables. Let D = S – T. What is the probability that Soledad sends more texts on a randomly selected day? 0.104 0.214 0.786 0.896The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls. Use the range rule of thumb to identify a range of values that are not significant. a. The maximum value in this range is (Round to one decimal place as needed.) b. The minimum value in this range is (Round to one decimal place as needed.)