The marginal distributions of two random variables X and Y, together with some values of their joint distribution, are given in the table below. Fill in the table in such a way that X and Y are independent random variables. Y= -3 Y= -2 Y= 3 X= -3 0.08 0.20 X=1 0.32 0.80 0.40 0.40 0.20 1.00
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- Side-by-Side University of Southern California Schaeffer Center for Find the probability distribution for X. Round to four Health Policy and Economics, researchers concluded that decimal places. customers overpaid for prescriptions 23% of the time. This overpayment often occurs because the copay is higher than the full cost of a drug. Suppose four prescriptions are selected at random. Let X be a random variable defined to p(0) = be the number of prescriptions for which the customer overpaid. p(1) = p(2) = p(3) = p(4) = 27% 75°FLet x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. x 63 79 70 80 84 87 y 46 49 45 55 57 58 Find Se from the data.Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 13 22 13 13 7 12 23 19 11 9 13 4 The sample mean is x = 12.4%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μ ≠ 11%; H1: μ = 11%; two-tailedH0: μ = 11%; H1: μ ≠ 11%; two-tailed H0: μ = 11%; H1: μ < 11%; left-tailedH0: μ = 11%; H1: μ > 11%; right-tailed (b) What sampling distribution will you…
- Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 16 6 8 9 10 18 14 13 9 10 25 18 13 8 14 3 The sample mean is x = 12.1%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use ? = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)For a continuous random variable x, the population mean and the population standard deviation are 139 and 9, respectively. You take a simple random sample of 36 elements from this population. The mean of the sampling distribution of the sample mean is:A random variable X has a binomial distribution with q = 0.34 and a sample size of n. Find the mean and variance for the random variable Y which is defined below. Y = nX Mean: __________________ Variance: __________________
- Part 2 Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.338 0.306 0.340 0.248 0.367 0.269 y 3.5 7.7 4.0 8.6 3.1 11.1 Σx = 1.868, Σy = 38, Σx2 = 0.592034, Σy2 = 294.32, Σxy = 11.1556, and r ≈ -0.901. Se ≈ 1.5890, a ≈ 26.420, and b ≈ -64.517. (a) Find the predicted percentage of strikeouts for a player with an x = 0.328 batting average. (Use 2 decimal places.) %(b) Find a 90% confidence interval for y when x = 0.328. (Use 2 decimal places.) lower limit % upper limit %Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance a. Consider the bivariate distribution for the random variables x and y. The correlation coefficient of x and y is the covariance b. multiplied by the product of the standard deviations for x and y. c. multiplied by the standard deviation of y and divided by the standard deviation of x. d. multiplied by the standard deviation of x and divided by the standard deviation of y.Nationally, about 11% of the total U.S. wheat crop is destroyed each year by hail.† An insurance company is studying wheat hail damage claims in a county in Colorado. A random sample of 16 claims in the county reported the percentage of their wheat lost to hail. 15 7 7 13 13 20 13 12 5 10 26 22 13 7 11 3 The sample mean is x = 12.3%. Let x be a random variable that represents the percentage of wheat crop in that county lost to hail. Assume that x has a normal distribution and σ = 5.0%. Do these data indicate that the percentage of wheat crop lost to hail in that county is different (either way) from the national mean of 11%? Use α = 0.01. (a) What is the level of significance? Compute the z value of the sample test statistic. (Round your answer to two decimal places.)(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)