Concept explainers
Suppose that Y is a discrete random variable with
- a. Do you expect the mean of X to be larger than, smaller than, or equal to µ = E(Y)? Why?
- b. Use Theorems 3.3 and 3.5 to express E(X) = E(Y + 1) in terms of µ = E(Y). Does this result agree with your answer to part (a)?
- c. Recalling that the variance is a measure of spread or dispersion, do you expect the variance of X to be larger than, smaller than, or equal to σ2 = V(Y)? Why?
- d. Use Definition 3.5 and the result in part (b) to show that
that is, X = Y + 1 and Y have equal variances.
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Mathematical Statistics with Applications
- For the following table of data. x 1 2 3 4 5 6 7 8 9 10 y 0 0.5 1 2 2.5 3 3 4 4.5 5 a. draw a scatterplot. b. calculate the correlation coefficient. c. calculate the least squares line and graph it on the scatterplot. d. predict the y value when x is 11.arrow_forwardRespiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forward
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