Find a general formula using p and q for P(reach 5 | X(0) = 3)
a. P(X=3)=
b. P(X=3)=
c. P(X=0)=
d. P(X=3)=
Please include Excel formula.
Determine the following probabilities. a. If n 4, N 12, and A 5, find P(X 3). b. If n 4, N 6, and A 3, find P(X 3) c. If n 6, N 11, and A 5, find P(X 0) d. If n 3, N10, and A 3, find P(X 3)
3. The roots of the equation x2 +2px - q = 0, where p and q are given data, can be found using the quadratic formula, so x = -p+ Vp+q. Study the conditioning of this formula with respect to changes in p and q separately.
6. [Marks 3] Suppose p and q are distinct primes. Find the general solution to the set of equations: x= -1 mod p x = -1 mod q. Show all the steps/details.
5. (10 points) Let p="x < y", q="x < 1", and r="y > 0". Using ~, 1, V write the following statements in terms of the symbols p, q, and r. (a) 0 <y < x < 1. (b) 1 < x <y<0.
(1 point) Use the inner product <p.q >= P(-3)(-3) + p(0)q(0) + p(2)q(2) in Pg to find the orthogonal projection of p(x) = 2x2 + 6x + 4 onto the line L spanned by 9(x) = 3x2 - 4x - 6. proj. (p) =
Using the Poisson tables (or formula, or Excel...), find P(X = 5) if the mean is 3.6. a. 0.4319 b. 0.8441 c. 0.2114 d. 0.1377 e. 0.5132
Given the Transition Diagram, find P(X(n)=5 |
X(0)=3)
0 4
3. Find a general solution of the system X' = AX with 3 0 0 -3 4 (1) A (2) A = 0 2 0 (3) A 6 -5 4 0 1 -3 0 3 -5 0 5 0 0 -1 1 (4) A [1 7 4 -5 3 (5) A = 3 -5 -3 5 5 -1 3 (6) A 1 0 0 0 2 2 0 0 0 3 3 0 0 0 4 4
Use the variation of parameters formula to find a general solution of the system x'(0) AX(t) + f(t), where A and f(t) are given -4 2 А. FU) 21 12 +21 Let x(t) = xy()+ X(t), where x, (t) is the general solution corresponding to the homogeneous system, and X(t) is a particular solution to the nonhomogeneous system. Find X. (t) and X.(1).
Q #1 (2 marks) Find the general solution for the DExy'-ymx1y, x>0, y>0.