Section I 1. Consider a discrete random variable X with pmf summarized in the table below. -3 4. f(x) 0.45 0.3 0.25 (a) deviation o of X. Compute the mean µ, the variance o?, and the standard
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A: Answer Given The population mean= 4.78This is left-tailed test.
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- Suppose you have a sample of 9 observations Y1,...,Y, from a normal population with mean 2 and variance 4. Let Y and S denote the sample mean and sample variance, respectively. What is the distribution of E ( (a) (b) 653 (c) Suppose X1,X2, X3, X4, X5 are independent random variables from a normal population with mean 0 and variance 4. Define S3 = E(X, - X). What is the distribution of 253 + S3?Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. A. What is the variance of the sample mean Xn? B. Use your answer to part (A), and Chebyshev’s inequality, to come up with a quantitative upper bound for the probability that sample mean Xn is more than a certain distance of 175Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.78. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (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) Do the given data indicate that the population mean RBC count for this patient is lower than 4.78? Use ? = 0.05. (a) What is the level of significance?State the null and alternate hypotheses. H0: ? < 4.78; H1: ? = 4.78H0: ? = 4.78; H1: ? ≠ 4.78 H0: ? = 4.78; H1: ? < 4.78H0: ? = 4.78; H1: ? > 4.78H0: ? > 4.78; H1: ? = 4.78 (b) What sampling…
- The mean and standard deviation of a random variable x are 9 and 4 respectively. Find the mean and standard deviation of the given random variables: (1) y = x + 3 O = (2) v = 5x (3) w 3 5х + 3 O = ||X is a normally distributed random variable with a mean of 5 and a standard deviation of 2. For which value of a is P(X > a) = 0.6293? What is a?If X is a negative binomial rv, then Y= r+Xis the total number of trials necessary to obtainr S’s. Obtain the mgf of Y and then its mean valueand variance. Are the mean and variance intuitively consistent with the expressions for E(X)and V(X)? Explain
- Let x be a random variable that represents red blood cell count (RBC) in millions of cells per cubic millimeter of whole blood. Then x has a distribution that is approximately normal. For the population of healthy female adults, suppose the mean of the x distribution is about 4.64. Suppose that a female patient has taken six laboratory blood tests over the past several months and that the RBC count data sent to the patient's doctor are as follows. 4.9 4.2 4.5 4.1 4.4 4.3 (1) 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) Do the given data indicate that the population mean RBC count for this patient is lower than 4.64? Use a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. Ο Hg: μ= 4.64; H1: μ 4.64 Ο Ηρ: μ> 4.64; H1: μ = 4.64 Ho: u = 4.64; H1: u * 4.64 (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. O…Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ∼ N (85, 25)). step1: Let M = aX + b for some constants a, b not equal to 0. Write an expression for the pdf of M . step 2: Suppose that X represents an approximate distribution of the final scores in a certain math course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the teacher were to curve the scores, it means he would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose he wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should he choose for a and b? What students would see their score lowered, and what students would see their score increased?Compute the standard score (Z-score) for x, when x = 21, the mean of the distribution = 27, and the variance (S2) = 9. Z = %3D O 2 -2 .67 -.67
- 1.Find the expected value E(X) 2.find the variance 3.find standard deviation 4.find the value of P(X<8) round all answers to one decimalLet ex be a random variable that represents the hemoglobin count (HC) in human blood (measured in grams per milliliter). In healthy adult females, x has a approximately normal distribution with a population mean of 14.0 and population standard deviation equal 2.3. Suppose a female patient had 10 blood test over the past year , and the sample mean HC was determined to be 15.3. With a level of significance a= 0.05, determine whether the patient's HC is higher than the population averages. Specifically do the following: write the data state null hypothesis H0 and the alternate hypothesis H1
