1. Two close friends live in different states. The probability mass function for the number or meetings of two friends in a one-year period is given by random variable X is as follows: x = 1, 2,3,4 P(X =x)={3) else Rewrite this pmf in a table form. b. Determine the 'c' value so that the function given is a valid probability mass function. Justify your answer by showing that the pmf is valid. Derive the cumulative density function (cdf) - present it in functional form like this a. с. some#1 x< smthl some#2 smthl
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- Please answer page 143, 2.6.6.Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is gbb, then =Rgbb1. Suppose that the random variable X is defined in terms of R as follows: =X−2R−R22. The values of X are given in the table below. Outcome ggb gbb bgb bbb bbg bgg ggg gbg Value of X −2 −1 −1 −2 −1 −2 −5 −2 Calculate the values of the probability distribution function of X , i.e. the function pX . First, fill in the first row with the values of X . Then fill in the appropriate probabilities in the second row. Value x of X pXxLet x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 17 16 18 15 12 14 17 17 11 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) x = s = (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. a: μ = 14; H1: μ < 14 b: μ = 14; H1: μ ≠ 14 c: μ > 14; H1: μ = 14 d: μ < 14; H1: μ = 14 e: μ = 14; H1: μ > 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since we assume…
- Given the following probability distribution for the number of semesters of Math a (non-Math major) college student will take as they earn their degree: x:number of semesters of Math 1 2 3 4 P(x) 0.25 0.45 0.20 0.10 What is the probability that a randomly selected (non-Math major) college student will have taken exactly 3 semesters of Math? Show how you calculated your result here (type in what you typed on your calculator or computer, etc) Calculation: __________ Now type in your final simplified or rounded answer, if necessary round your answer to four decimal places. P(exactly 3 semesters of Math) = _____________Answer 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 sackLet x be a random variable that represents hemoglobin count (HC) in grams per 100 milliliters of whole blood. Then x has a distribution that is approximately normal, with population mean of about 14 for healthy adult women. Suppose that a female patient has taken 10 laboratory blood tests during the past year. The HC data sent to the patient's doctor are as follows. 14 18 15 19 13 11 15 18 15 12 (i) Use a calculator with sample mean and standard deviation keys to find x and s. (Round your answers to two decimal places.) X = S = (ii) Does this information indicate that the population average HC for this patient is higher than 14? Use a = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. О Но: и 3D 14;B Hі: и 14; Hі: и %3D 14 Но: и 14 О Но: и 3D 14;B Hi: и # 14 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O The standard normal, since we assume that x has a normal distribution and o is…
- Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of “girls” (g) and “boys” (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is bbb, then R(bbb)=0. Suppose that the random variable X is defined in terms of R as follows: X=R^2-2R-1. The values of X are given in the table below.b. 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.Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" (g) and "boys" (b), which we write gbg, bbb, etc. For each outcome, let R be the random variable counting the number of girls in each outcome. For example, if the outcome is bbg, then R(bbg) = 1. Suppose that the random variable X is defined in terms of R as follows: X=R- - 2R-4. The values of X are given in the table below. Outcome bbb ggb bbg gbg gbb bgg bgb gg Value of X-4 -4 -5 -4 -5 -4 -5 -1 Calculate the values of the probability distribution function of X, i.e. the function py. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row. Value x of X Px (x) E 1:48 PM 3/21/2022 hp Compag LAI956X 立
- Suppose X and Y are two independent random variables with: X Y mean 2 -4 st dev 3 3 The mean of X+Y is .The standard deviation of X+Y is (to two places after the decimal).Which of the following is a continuous random variable? A)The number of students arrives to the library checkout desk before noon time. B)The number of students waiting in the cafeteria lane for lunch. C)The travel time of a bus between two cities. D)The number of newspapers sold on a specific date. E)The number phone calls received by call center for a certain period of time.1. If a random variable X takes the value 1,2,3,4 suchthat 2P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4).Find the probability distribution of X.