Are K=10, C=1 valid witnesses to show that f(x)=10 is O(x)?
f(n) = O(g(x)) means there are positive constants c and k, such that 0 ≤ f(x) ≤ cg(x) for all x ≥ x0 10 = O(x) => 10 <= cx Let's assume c = 1 => 10 <= cx => 10 <= 1*x => 10 <= x it's true for all x >= 10 so, 10 = O(x) given c = 1 and k = 10
2. (10 points) Given the following functions: f()= r* - 50x3 +1, g(x) = 24 Show that f(x) = N(g(2) using the definition of 10. Do not forget to provide the witnesses.
Question 17 10 pts Determine the value of c such that f(x, y) is a valid joint pmf of the random variables X and Y, given the values for the joint pmf below Y-2 Y 4 Y=6 X-1 0.05 0.01 0.13 X-2 0.10 0.08 0.04 X -3 0.05 0.13 C OD.41 O O.82 O 0.14 O 0.07 Question 18 10 pts Aprivately owned liquor store operates botha drive-in facility and a walk-in facility. On a randomly selected day, let Xand...
Q3 (Prove that P∞ k=1 1/kr < ∞ if r > 1) . Let f : (0,∞) → R be a twice differentiable function with f ''(x) ≥ 0 for all x ∈ (0,∞). (a) Show that f '(k) ≤ f(k + 1) − f(k) ≤ f '(k + 1) for all k ∈ N. (b) Use (a), show that Xn−1 k=1 f '(k) ≤ f(n) − f(1) ≤ Xn k=2 f '(k). (c) Let r > 1. By finding...
2. Graph the functions f(x)x(x 1)(x-2) ..(x- k) for k- 1,2,..,10. (These are examples of the polynomials occurring in the error formula for polynomial interpolation.) We want to produce an evenly spaced table of values for the function f(x) sin(x) for x E [O,T/2] such that, with cubic interpolation, we can give the values of the function at any point in the interval with an error less than 5 10-12. That means finding a number n such that with h-/2n...
solve for c such that f(x,y) is a valid density function. Seiten f(x, y) = 1<x<y <3 otherwise 0,
Phthalic acid (H,C,H,O,) is a diprotic acid with K 1 = 1.12 x 10- and K 2 = 3.90 x 10-Determine the pH of a 0.177 M phthalic acid (H,C,H,O,) solution. pH = about us Career P o licy Terms of use contacts 12.50
Let N denote a nonnegative integer-valued random variable. Show that k-1 k O In general show that if X is nonnegative with distribution F, then and E(X") = : nx"-'F(x) ds.
QUESTION 3 To show that f(x) is O(g(x) using the definition of big o, we find Cand k such that f(x) < Cg(x) for all x > k. QUESTION 4 Finding the smallest number in a list of n elements would use an OU) algorithm.
Need it urgently Expand the function, f(x) = x cosx in a Fourier series valid on the interval -1 <x<t. You must show the details of your work neatly.
f(x) = *, x = 1, 2, 3, 4 © Verify that f(x) is a valid probability mass function(pmf). © P(X < 2.5) * P(X > 1) © Compute the mean and variance