X1 and X2 are indep N(0,1) random variables. Y1=(X1+X2)/2 and Y2={(X1-X2)^2}/2. let 1. find the mgf of Y2 2. find the jpdf of Y1 and Y2. 3. find the marginal pdf of Y1 and Y2.
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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 following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.
- Let X and Y have the joint pdf f(x,y)= x+y , 0<=x<=1, 0<=y<=1. Calculate the mean(x) mean (y) variance (x) variance(y)Let X1 and X2 be IID exponential with parameter > 0. Determine the distribution ofY = X1=(X1 + X2).Suppose that the random change in value of a financial asset is X over the first day and Y over the second. Suppose also that Var(X) =18 and Var(Y) = 26 In this case, the total change in the value over these two days is given by X +Y. Do you have enough information to compute Var(X +Y)? If so, compute this value. If not, explain what additional information you need to do so.
- The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34. Calculate Var(X+Y) with a full explanationCalculate correlation coefficient from the following results : N 10 ΣΧ 100 ΣΥ- 150 E(X-10}²= 180, 2(Y-15)' = 215 E(X-10(Y-15) = 60. %3DSuppose that f(x) = 0.125x for 0 < x < 4 Determine the mean and the variance of X.
- Let Y be a random variable with pdf f(y)= (1/18)(y^3−1) for 1<y<3.(a) Calculate P (Y > 2.5).(b) Calculate the variance of Y .Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Bb UTF Bb UTF Bb Sigi 2 Sta Bb E Rep 9 Nev Bb UT Rep Bb UTF Bb UTF Bb Mic * Win ent.blackboardcdn.com/5df8324563085/7628679?X-Blackboard-Expiration=1645045200000&X-Blackboard-Signature%3D BIU A A- | 三= Fill out the table below and calculate the x statistic and degrees of freedom. Blackjack Preserve Winthrop Woods Glencarin Garden Observed 54 48 24 d.f. = If you conduct this analysis in R, the output tells you the p-value = 0.002. What conclusion can you make? Explain how you reached this conclusion.
