Suppose that the random variable X represents the length of a punched part in centimeters. Let Y be the length of the part in millimeters. If E(X) = 4 and V(X) = 0.25, what are the mean and variance of Y? Mean = i mm Variance = i mm²
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- Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 50 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that ? = 7.20 ml/kg for the distribution of blood plasma.Properties of scaling. Suppose that you want to examine the relationship between wages and experience measured in months rather than years. a) What is the variance of experience in months? Compare this to 1b). b) What is the covariance of wages and experience in months? Compare this to 1d). c) What is the correlation of experience and wages? Compare this to le). d) Prove mathematically that the Corr(cX,Y) = Corr(X,Y) using the properties of summation from class. Show each step of your proof.The thickness of a flange on an aircraft component is uniformly distributed between 0.95 and 1.05 millimeters. (a) Determine the proportion of flanges that exceeds 0.99 millimeters. (b) What thickness is exceeded by 90% of the flanges? ! millimeters (c) Determine the mean and variance of flange thickness. Mean = ! millimeters Variance = i millimeters? (Round your answer to 6 decimal places.)
- The amount of nicotine in a cigarette produced by a tobacco company is a random variable with mean 2.2 mg and standard deviation 0.3 mg. Taking 100 randomly chosen cigarettes, let X; denote the nicotine content of the ith cigarette for i = 1,..., 100, and let X = 100 Ei=1 X; be the sample mean of the nicotine content. 100 a. What is the variance of X? Var(X) = Approximate the probability that X is higher than 2.25 in terms of the standard normal random variable. (The answer is given in terms of 2.25, standardized by mean and standard deviation of X.) P(X> 2.25) = P(Z >Using a long rod that has length m, you are goingto lay out a square plot in which the length of eachside is m. Thus the area of the plot will be m2.However, you do not know the value of m, soyou decide to make n independent measurementsX1, X2,... Xn of the length. Assume that each Xihas mean m (unbiased measurements) and variance s2.a. Show that X2 is not an unbiased estimatorfor m2. [Hint: For any rv Y, E(Y2) ¼V(Y) + [E(Y)]2. Apply this with Y ¼ X.]b. For what value of k is the estimator X2 - kS2unbiased for m2? [Hint: Compute E(X2 - kS2).]An analysis of variance produces SSbetween = 30, SSwithin = 60. Df between is 2 and df within is 15, For this analysis, what is the F-ratio? a. 30/60 = 0.50 c. 15/4 = 3.75 b. 60/30 = 2.00 d. 4/15 = 0.27
- The maximum patent life for a drug is 17 years. Subtracting the length of time required by the FDA for testing and approval of the drug provides the actual patent life for the drug that is, the length of time that the company has to recover research and development costs and to make a profit. The distribution of the lengths of actual patent lives for new drugs is given below, where Y is a random variable representing actual patent life of a drug (in years): y P(Y=y) F(y) 4 5 6 7 8 9 10 11 0.06 0.08 0.11 0.15 0.22 0.18 0.12 0.08 a) Complete the table above with the cumulative probability distribution for actual patent life (F(y) = P(Y ≤ y)). b) What is the probability that the actual patent life of a random drug is 6 years or less? c) What is the probability that the actual patent life of a random drug is more than 8 years? Show this in two ways: i. using the probability distribution for Y ii. using the cumulative probability distribution for Y, and applying our probability of comple-…X and Y are independentPlease only typing answer and explain step by step