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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.Q3/(a) Let X = b(n,) and E(x)= E(16-7x) find n. (b)Let X be a random variable with p.d.f, ƒ(x)= c 3 x=1,2,3,.., zero elsewhere. Find the constant c.Q3/(a) Let X = b(n, ) and E(x)=E(16–7x) find n. (b)Let X be a random variable with p.d.f, f(x)=c x =1,2,3,.., zero elsewhere. Find the constant c.
- A random variable X takes values 0,1,2 where E(x) =1.5, var(x)=0.25 then E (3x– x² +4) =A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1).Find its mean value and variation.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.
- If X is a random variable with pdf f(x) = 2x − 2 where x = (1, 2), find the variance of Y = 2X - 3.X and Y are two independent random variables with fy (x) eX-u (x) and fy (V) = e. u (y). Find the mean of the random variable Z= X - Y for X> Y for. X< YQ2: (b) Let X₁, X2, X3 be uncorrelated random variables, having the same variance o². Consider the linear transformations Y₁ = X₁ + X₂, X2 + X3. Find the correlations of Y₁, Y; i, Y₂ = X₁ + X3 and Y3 for i + j. =
- Suppose X and Y are two random variables with E[X] = 1, Var (X) = 4, E[Y ] = -1, Var (Y) 4, and Cov (X, Y) = 1. Find the standard deviation of (X - Y). = (a) 2 (b) √2 (c) 6 (d) √6 (e) None of the aboveX is a continuous random variable having p.d.f. f(x) such that f(x) = kr Osx55 otherwise Find : (a) the constant k; (b) P(15XS 2); (c) (d (e) (f) E(X); E(3X + 1); E(X?); Var (X); (g) Var (4X - 5);If X is a Poisson variable such that P(X =2) = 9P(X= 4) + 90P(X = 6), find the mean and variance of X.
