7. Let x(t) be a Poisson process having rate 6 5. a) P(X(1)=2] b) P(X(2) = 31x(1)s 2] c) P(X(2) = 31x(4) = 5] d) EIX(1)] e) Var[X(1)] (1D 7. Let x(t) be a Poisson process having rate 6 5. a) P(X(1)=2] b) P(X(2) = 31x(1)s 2] c) P(X(2) = 31x(4) = 5] d) EIX(1)] e) Var[X(1)] (1D
let f:IR-DIR be defined by f(x) = 31x), Prove that f(x)-31x1 is invertible. Compute the preimage f'((2,4]).
6. Solve the following boundary value problem: 1 U = 34xx, 0 < x < 1,t> 0; u(0,t) = u(1,t) = 0; u(x,0) = 7 sin nx - sin 31x
6. (20) Consider the table X 02 3 y = f(x) 7 11 -4 (a) Fit the given data with a quadratic spline. (b) Find an approximate value of f(3) using the first-degree spline. 6. (20) Consider the table X 0 | 2 | y = f(x) | 7 11 | 3 5 (a) Fit the given data with a quadratic spline. YE (b) Find an approximate value of f (3) using the first-degree spline.
If ice homogeneously nudeates at-28.5 ℃ calculate the critical radius given values of-31x 108 l/m3 and 25 x 10-3 נ/m2, respectively, for
x y 5 6 6 9 7 11 8 13 9 14 10 15 11 15 12 13 a) Generate a model for y as a function of x b) Is this model useful? Justify your conclusion based on i) R2 adjusted, ii) Hypothesis test for model coefficient, iii) overall model adequacy test and iv) regression assumptions c) If needed, modify model as appropriate and generate the new model. *Complete all parts of the problem please, be as detailed with...
8. 2 sinº x-3 sin x-1=0 11. 4 sin’ x + 7 sin x = 6 9. tanx-1=0 12. ( tan x-)(tan x-3) = 0
The graph of f(x) is given below: 11 godina osno obs 11-10-9-8 -7 -6 -5 4 -3 -2 - 1 2 3 4 5 6 7 8 9 10 11 12 a-Draw a tangent to the given figure for x=9 and explain in a few words what this line tells us about the curve of the function f(x). b. In the interpretation of f19), it is said that the result oives an approximation of the function asx is increased by...
[6 points] Suppose that f'(x) = 3x2 + 2x + 7 and f(1) = 11. Find the function f(x). Of(x) = x3 + x2 + 7x + 11 Of(x) = x3 + x2 + 7x + 2 Of(x) = 6x + 5 Of(x) = x3 + x2 + 9 10. V MY NOTES [6 points] Find the integral: 15x3/2 + 21n|x[ + c 10 x3/2 + 2\n\xl + C O 5x1/2 - + c şx-1/2 - + c
28 The following is a sample of 25 measurements. L02098 7 6 6 11 8 9 11 9 10 8 7 7 5 9 10 7 7 7 7 9 12 10 10 8 6 a. Compute , s2, and s for this sample b. Count the number of measurements in the intervals e ± s, x ± 2s, and x ± 3s. Express each count as a percentage of the total number of measurements. c. Compare the percentages found...