Core 2 Revision Sh
... Substitute in number and zero comes out as it’s a factor. No remainder. If f(3x3 - 2x2 + x –6) and x-3 is a factor, then take out (x-3) to leave (x-3)(ax2 + bx + c) = 0 and compare coefficients to find a, b and c then solve for the quadratic. If don’t know any factors, experiment with numbers to fin ...
... Substitute in number and zero comes out as it’s a factor. No remainder. If f(3x3 - 2x2 + x –6) and x-3 is a factor, then take out (x-3) to leave (x-3)(ax2 + bx + c) = 0 and compare coefficients to find a, b and c then solve for the quadratic. If don’t know any factors, experiment with numbers to fin ...
Sequences
... You get the sequence 1,2,3,…. on the "strip" at the right Drag this strip to the left most position of the "workspace" Drag the multiplication-sign (an asterix) to the position right of the strip. Change the big 5 on the right side to a 3. Drag this 3 to the position right of the multiplication-sign ...
... You get the sequence 1,2,3,…. on the "strip" at the right Drag this strip to the left most position of the "workspace" Drag the multiplication-sign (an asterix) to the position right of the strip. Change the big 5 on the right side to a 3. Drag this 3 to the position right of the multiplication-sign ...
In Discrete Time a Local Martingale is a Martingale under an
... We consider a discrete-time infinite horizon model with an adapted d-dimensional process S = (St ) given on a stochastic basis (Ω, F, F = (Ft )t=0,1,... , P ). The notations used: M(P ), Mloc (P ) and P are the sets of d-dimensional martingales, P local martingales and predictable (i.e. (Ft−1 )-adap ...
... We consider a discrete-time infinite horizon model with an adapted d-dimensional process S = (St ) given on a stochastic basis (Ω, F, F = (Ft )t=0,1,... , P ). The notations used: M(P ), Mloc (P ) and P are the sets of d-dimensional martingales, P local martingales and predictable (i.e. (Ft−1 )-adap ...
LECTURE 10 COMPLEX NUMBERS While we`ve seen in previous
... Somehow, to each square matrix we’ll attach a polynomial in one variable, whose degree is the number of columns (or equivalently, the number of rows). So to find the eigenvalues of a 2x2 matrix just requires us to solve a quadratic equation, which is trivial by the quadratic formula. ...
... Somehow, to each square matrix we’ll attach a polynomial in one variable, whose degree is the number of columns (or equivalently, the number of rows). So to find the eigenvalues of a 2x2 matrix just requires us to solve a quadratic equation, which is trivial by the quadratic formula. ...
PRESENT STATE AND FUTURE PROSPECTS OF STOCHASTIC
... problems lead to problems in other fields, in differential and integral equations, for example, which can be formulated and solved with little or no knowledge of the probability background. On the other hand, there are the peculiarly probabilistic problems, say on the convergence of mutually indepen ...
... problems lead to problems in other fields, in differential and integral equations, for example, which can be formulated and solved with little or no knowledge of the probability background. On the other hand, there are the peculiarly probabilistic problems, say on the convergence of mutually indepen ...
ppt
... terminate when q = 5x * 2y, where x and y are positive integers. Essentially, this means that the expansion will terminate if q is a multiple of 5 or 2, or a combination of multiples of 5 and 2. Any other value of q will cause the decimal expansion to repeat indefinitely. To establish this conjectur ...
... terminate when q = 5x * 2y, where x and y are positive integers. Essentially, this means that the expansion will terminate if q is a multiple of 5 or 2, or a combination of multiples of 5 and 2. Any other value of q will cause the decimal expansion to repeat indefinitely. To establish this conjectur ...
1 - intro to sequences.notebook
... Consider the sequence given by a "plus 8" pattern: 2,10,18,26,... John says that the formula for the sequence is f(n) = 8n + 2. Jennifer tells John that he is wrong because the formula for the sequence is f(n) = 8n 6. ...
... Consider the sequence given by a "plus 8" pattern: 2,10,18,26,... John says that the formula for the sequence is f(n) = 8n + 2. Jennifer tells John that he is wrong because the formula for the sequence is f(n) = 8n 6. ...
Document
... A sequence {an} converges to L (a real number) if, given any positive distance from L, we can go far enough out in the sequence so that every term from there out is within that given distance from L. We write limnan = L or {an} L . If {an} does not converge, we say it diverges. ...
... A sequence {an} converges to L (a real number) if, given any positive distance from L, we can go far enough out in the sequence so that every term from there out is within that given distance from L. We write limnan = L or {an} L . If {an} does not converge, we say it diverges. ...
Slide 1
... A sequence {an} converges to L (a real number) if, given any positive distance from L, we can go far enough out in the sequence so that every term from there out is within that given distance from L. We write limnan = L or {an} L . If {an} does not converge, we say it diverges. ...
... A sequence {an} converges to L (a real number) if, given any positive distance from L, we can go far enough out in the sequence so that every term from there out is within that given distance from L. We write limnan = L or {an} L . If {an} does not converge, we say it diverges. ...
View slides
... For all integers n we have ˆ ( n ) C 0 uniformly for n N . Taking y n , we obtain ˆ ( y ) 0 as y , and hence L1 (R). ...
... For all integers n we have ˆ ( n ) C 0 uniformly for n N . Taking y n , we obtain ˆ ( y ) 0 as y , and hence L1 (R). ...
The Gaussian distribution
... Convolutions Gaussian probability density functions are closed under convolutions. Let x and y be d-dimensional vectors, with distributions p(x | µ, Σ) = N (x; µ, Σ); ...
... Convolutions Gaussian probability density functions are closed under convolutions. Let x and y be d-dimensional vectors, with distributions p(x | µ, Σ) = N (x; µ, Σ); ...
THE FIRST COEFFICIENT OF THE CONWAY POLYNOMIAL
... In this paper we shall give a formula for a0 = VL(0) which depends only on the linking numbers of L. We will also give a graphical interpretation of this formula. It should be noted that the formula we give was previously shown to be true up to absolute value in [3]. The author wishes to thank Hitos ...
... In this paper we shall give a formula for a0 = VL(0) which depends only on the linking numbers of L. We will also give a graphical interpretation of this formula. It should be noted that the formula we give was previously shown to be true up to absolute value in [3]. The author wishes to thank Hitos ...
Topics for Review:
... a. Find the remaining sides and angles. b. Find the area. 11. Suppose that the depth of the water in a harbor is 20 feet at low tide, 30 feet at high tide, and fluctuates in such a way that it can be modeled with a sinusoidal function. Let t represent time measured in hours, and let D(t) represent t ...
... a. Find the remaining sides and angles. b. Find the area. 11. Suppose that the depth of the water in a harbor is 20 feet at low tide, 30 feet at high tide, and fluctuates in such a way that it can be modeled with a sinusoidal function. Let t represent time measured in hours, and let D(t) represent t ...
Document
... Suppose we have some vector A, in the equation Ax=b and we want to find which vectors x are pointing in the same direction (parallel) after the transformation. These vectors are called Eigenvectors. The vector b must be a scalar multiple of x. The scalar that multiplies x is called the Eigenvalue. ...
... Suppose we have some vector A, in the equation Ax=b and we want to find which vectors x are pointing in the same direction (parallel) after the transformation. These vectors are called Eigenvectors. The vector b must be a scalar multiple of x. The scalar that multiplies x is called the Eigenvalue. ...