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- Take a=1 in the questionA person's level of blood glucose and diabetes are closely related. Let x be a random variablemeasured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a12-hour fast, the random variable x will have a distribution that is approximately normal withmean μ = 84 and standard deviation of σ = 26 What is the probability that, for an adult after a12-hour fast, x is less than 81? Group of answer choices 0.546 0.454 0.023 0.273 0.227A4. If random variables X and Y each have variance o? = 3 and corr(X,Y) = 0.4, what is the value of Cov(3X – 1, 2Y + 2)?
- Compute for the variance and standard deviation of the population7. Assume that X and Y have a bivariate normal distribution having means 14.l and 1.3, and standard deviations 2.5 and 0.1, respectively, with correlation coefficient 0.8. Find P(Y >1.4|X =15) and P(X >15|Y = 1.4).Find the first two moments about the mean for the random variable X defined by X = -2 with prob. 1/3 3 with prob. 1/2 = 1 with prob. 1/6. %3D
- 26 The table to the right shows the cost per ounce (in dollars) for a random sample of toothpastes exhibiting very good stain removal, good stain removal, and fair stain removal. At α=0.01, can you conclude that the mean costs per ounce are different? Perform a one-way ANOVA test by completing parts a through d. Assume that each sample is drawn from a normal population, that the samples are independent of each other, and that the populations have the same variances. Very good stain removal Good stain removal Fair stain removal 0.37 0.75 0.60 0.49 2.66 1.18 0.33 0.46 0.46 1.64 0.33 0.50 0.58 0.41 1.39 (b) Identify the degrees of freedom for the numerator and for the denominator, determine the critical value, and determine the rejection region. The degrees of freedom for the numerator, d.f.N, is ____ and the degrees of freedom for the denominator, d.f.D, is _____ The critical…If the random variable X as a mean of u and a variance of o2 what is the P((X-u)² < 20): O less that equal to 1/4 O greater than or equal to 3/4 cannot tell O equal to 5/4Suppose that the random variable X has a Gamma Distribution with parameters a = 2 and B 2 where ·1 > 0 The variance of the random variable X, oy, is
- Let the random variables X and Y have the joint p.m.f. x+ y f (x, y) = 32 x = 1, 2, y = 1,2,3,4. Find the means lx and uy, the variances oy and oý, and the correlation coefficient p. Are X and Y independent or dependent? 6.A,b,c,d.Prob.5 Find the mean, the median, and the mode of the random variable X with the following probability density functions: (a) Gaussian distribution with parameters μ and o². (b) Exponential distribution with parameter 1. (c) Beta distribution with a = 3 and b = 4. (d) Uniform distribution in the interval (a, b).
