4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y = (X1 + 2X2 + X3)^2. What is the mean and variance of Y?
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Let X1 ∼ N(μ = 2, σ^2 = 4), X2 ∼ N(μ = 1, σ^2 = 16), and X3 ∼N(μ = −4, σ^2 = 9). Let X1, X2, and X3 be independent and Y = (X1 + 2X2 + X3)^2. What is the
A random variable follows a Normal distribution with mean and variance
Random Variable | Mean | Variance |
X1 | 2 | 4 |
X2 | 1 | 16 |
X3 | -4 | 9 |
The random variables X1, X2 and X3 are independent
Given Y is another random variable
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- Respiratory 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.The lines of regression of y on x and x on y are, respectively, y = x + 5 and 16x - 9y = 94. Find the variance of x if the variance of y is 16. Also, find the covariance of x and yY, = XB + ɛ, Show that the model variance in model Yi unbiased estimator of
- Consider (Y, X) values in a population as (8, 2), (9, 3), (10, 3), (12, 5), (14, 6), (16, 6) and (17, 8). Draw all possible samples from this population and compute Ratio estimator for each sample. Show that the ratio estimator is a biased estimator of population mean but has smaller mean square error as compared with the variance of mean per unit estimator.Find variance of y1 provide correct answera. Show that the regression R2 in the regression of Y on X is the squaredvalue of the sample correlation between X and Y. That is, show thatR2 = r2XY.b. Show that the R2 from the regression of Y on X is the same as the R2from the regression of X on Y. c. Show that ^β1 = rXY (sY/sX), where rXY is the sample correlationbetween X and Y, and sX and sY are the sample standard deviationsof X and Y.
- Two variables have the regression lines 3x + 2y = 26 and 6x + y = 31. Find the mean values, the correlation coefficient between x and y and the ratio of variances of the variables.Find the variance if X~N(0, 7) and 95% of the data are between -7 and 7.The regression lines between two random variables X and Y is given by 3X + Y = 10 and3X + 4Y = 12 .Find the correlation between X and Y.