Let G be the Prisoners Dilemma game with stage payoffs:
CDC2,20,3D3,01,1
Find the values of δ ε(0, 1) such that the tit-for-tat strategy can be sustained as a SPNE in the infinitely repeated PD G(infinity, 1)
Let G be a group of order 42.
Prove both (a) and (b).
Prove both (a) and (b).
Prove both (a) and (b).
7 . Let G be a group of order 42 .( a ) Prove that G has a normal subgroup of order 7 .`( b ) Prove that G is a semidirect product of a normal subgroup of order 21 and 2.2 .
Let G be a connected bipartite graph (i.e the set of vertices is split as X S Y so that the edges are connecting some pairs xi ∈ X with yj ∈ Y ). Show that if each vertex has multyplicity 3 then there is a complete matching( i.e the number of vertices in X is the same as in Y and there is matching of all vertices in X with vertices in Y )
Let Me Try Chapter 3 (Simnet)
Pause & Practice Chapter 3 (found in Chapter 3 of the textbook, submitted through Canvas)
Guided Project 3-3 (Simnet Blue Project Block – Simnet Graded)
Independent Project 3-4 (Simnet Blue Project Block – Simnet Graded)
Independent Project 3-4 (Simnet Blue Project Block – Simnet Graded)
Improve It Project 3-7 (found at the end of Chapter 3, submitted through Canvas)
Hello, can you please help me with this question. Thank you so much!
1 . Let [ : Man -> Min be defined by [ ( A ) = = ( A + AT )( a ) ( 5 points) Show that I is a linear operator on Man .( b ) ( 7 points ) Show that ker I is the subspace of all ~ x ~ skew – symmetric matrices .( c ) ( 8 points ) Show that range I is the subspace of all ~ x ~ symmetric matrices . ( Becareful about this part . )
Let L: IRn IRm be a linear mapping. What can we say about the injectivity, the surjectivity, & the bijectivity of L if:
a) n > m
b) n = m
c) n < m
Also, give a simple example for each case.
Let L be an n × n elementary unit lower triangular matrix, that is, L has 1’s on the maindiagonal, and zeros in all other positions except column k. The nonzero entries in column kappear in positions k to n (and the (k, k) entry is, as already mentioned, equal to 1). Assumethe following equation holds,P1*P2 · · · Pq*L = M*P1*P2 · · · Pq,where each Pi, i = 1, . . . q is a permutation matrix that encodes an exchange between rows liand mi, such that k + 1 <= li <= n and k + 1 <= mi <= n, and M is some other n × n matrix.Show that if the above equation holds, then M must also be an elementary lower triangularmatrix all of whose nonzero entries are either 1’s on the diagonal or lie in positions k to n ofcolumn k. Furthermore, show that the entries of column k of M must be precisely the entriesof column k of L after the q swaps given by Pq, . . . , P1 are applied to this column. In otherwords, show thatM(:, k) = P1 · · · PqL(:, k).Hint: Let Q = P1 *P2 · · · Pq. Write Q in block-matrix form, with two diagonal blocks of size k×kand (n − k) × (n − k) respectively and corresponding off-diagonal block. The first diagonalblock is known in closed form. Why? The two off-diagonal blocks are also known in closedform. Why? Use block matrix-multiplication to separately evaluate columns 1 : k and alsocolumns k + 1 : n of the left-hand side Q*L and the right-hand side M*Q and determine theform of M.
P = X + Y^2 + Z^3 + W^4, where
X_1, X_2, .., X_400Y_1, Y_2, .., Y_400Z_1, Z_2, .., Z_400W_1, W_2, .., W_400
are samples from Uniform(0,1) distribution. Find 90% confidence interval for the variance of P. Note: Use at least fifty thousand simulated samples to generate sampling distr. for the variance of P.
Please help me solve those questions, the questions are shown in the attachments (6, 7, 8)
5. LET L be a set in three – dimensional space and let LIL’I be equal to the Volume of’ `. if I has finite*volume . otherwise , let !It’s be undefined . Find Fizi .7 . For every one – dimensional set !’ for which the integral exists . Citi = To fluid , where flaj -Gril – Il, O _ _ _ I, zero elsewhere ; otherwise , let fic"; he undefined . Find Dic").16 ) [ 2 = 1 1 / 2) .8. Suppose the experiment is to choose a real number at random in the interval 10 . 1 1 . For any subinterval` , ` ) CID, I), it seems reasonable to assign the probablybability ?" [`, “] = 6 – a; Le, the probability ofselectin the point from the subinterval is directly proportional to the length of the subinterval . If thisis the case . choose an appropriate sequence of subintervals to shoe that Fall = " For all at 10. 1] .Hint : let It be a decreasing sequence of events , as in Question ? , then lim ,_ ta Pie! ! =Pllimn_ too Caj = Pill _; Cal
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