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f(x) = 2.10 Consider the following algorithm (known as Horner's rule) to evaluate -ax': poly = 0; for( i=n; i>=0; i--) poly = x * poly + ai a. Show how the steps are performed by this algorithm for x = 3, f(x) = 4x + 8x + x + 2. b. Explain why this algorithm works. c. What is the running time of this algorithm?
8. Let f (x) e, 0 > 0; x> 0 (1 1 +e (a) Show that f(x) is a probability density function (b) Find P(X> x) (c) Find the failure rate function of X
The cumulative distribution function of the random variable X is given by F(x) = 1-e-r' (z > 0). Evaluate a) P(X > 2) b) P(l < X < 3 c) P(-1 〈 X <-3). d) P(-1< X <3)
The random Variable X has a pdf fx (2) = {*** kr + > -1 <r<2 otherwise Y is a function of X and is derived using Y = g(x) = X S -X X2 X <0 X>0 Find: (A) fr(y) (B) E[Y] using fy(y) (C) EY] using fx (2)
Exercise 5. The joint probability density function of X and Y is given by (X,Y)=9) Scy-re-y if y> 0 and -y, y) O otherwise (a) Find c. (b) Find the marginal densities of X and Y. (c) Are X and Y independent?
What is the solution of day 2 dy 1(1+1) dx² + xăx x² y = f(x = a) (a > 0). on the interval 0<x< 0, subject to the boundary conditions y(0) = y(0) = 0? / is a positive integer.
1. Given the piece-wise function, 3x if x < 0 f(x)=x+1 if 0 < x 52 :- 2)2 if x>2 Evaluate f (__); f(0); f (); f(5)
Below is the p.d.f for the random variables X and Y, f(x,y)-36 0 otherwise Find the following probability Pr(x> 2) O 7/9 2/3 O 8/9
Suppose f is continuous, f(0)=0, f(2)=2, f'(x)>0 and f (x) dx = 1. Find the value of the integral fro f-?(x) dx =?
(b) Find an example of an open set G in a metric space X and a closed subset F of G such that there is no δ > 0 with {x : dist(x, F) < δ} C G