Prove the following (i) If G = & {4,N}, then E(§|G) = E(£) a.s.

Q: IX,- M |1+IX,-X Show that E →0 if and only if X X in probability.

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Q: E 27 F -> D] C. 44

A: Given : lenght  DC = 44, EF = 27 and AE = ED, BF = FC    To find : lengh of AB (x) ?

Q: 1. Find x, if 16 e4x = e16 (express answer in terms of In2 and integers)

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Q: A= 3 8 If what is A?

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Q: (a) In a certain state, license plates have two letters followed by three digits. How many such…

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Q: if L(e3t) = then L(S, e34 du) is. S-3

A: Formula:  If Lft=Fs, then L∫0ufudu=Fss. It is given that Le3t=1s-3. By the formula,…

Q: (a) Show that if n € N, then n+1 In dx. I

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Q: Integrate: / 82

A: Given integration is : ∫8x3lnxdx  To find the value of integration.

Q: .

A: We know that the exponential function ex has the Taylor's series expansion which is written as…

Q: とピ= ト-1

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Q: Is Statement (1) below True or False and WHY? TEA=B is equivalent to "TEA IFF TE B"

A: Let us provide justification and check whether both equations are equivalent or not

Q: . Show that n! > 3ª for n> 7.

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Q: 4. (4 – e 3*)³dx

A: Here we use the formula  ∫eaxdx=eaxa+C (a-b)3=a3-b3-3a2b+3ab2

Q: Let S = {1,2,3,4, 5}, G = {(1),(123), (132)}. For each element %3D a e S, find stabc(a) and orbg(a)

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Q: Reject Ho if |z| > N

A: We know that  Null hypothesis H0. Alternative hypothesis H1.

Q: Starting at a fixed time, each car entering an intersection is observed to see whether it turns left…

A: Given an experiment on observation of cars to see whether it turns leftL, rightR or goes straight…

Q: Show that, for all positive values of x and y, etty > e? ху

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Q: Show that for any n E N, 7(15".

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Q: If x[n]= {2,0,3,4}, x[(n-2),]= O a. {3,4,2,0} O b. {3,0,2,4} c. (2,4,3,0} O C.

A: The sequence is xn=2, 0, 3, 4. Then,  x0=2x1=0x2=3x3=4 Now, consider the sequence xn-24. Then, we…

Q: 8- 7- 6. -5-4 -3 -2 -1 -1 1 2 3 4 5 -2 Evaluate f(1) 4) 2.

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Q: (2) ylabäi For the function below ... the range * ?is (x + 1)3 y = (x² – 1) RO R/{3,-4} O R/{3,-3} O…

A: Given y = [(x+1)³] / [x²-1]    ---------(1) now we set  the denominator in (1) equal to 0 , to find…

Q: 1. Why is it important to recognize the converse and the con- trapositive of a conditional…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Simplify In(e-1) а. b. 5ogs ()

A: a. Simplify the expression as follows.

Q: If ro)-3"6 then f'(1)= O a. 18In(6)+ 12 O b. 18ln(6)+12in(3) Oc 18ln(6)+24ln(3). Od. 18ln(6)+24 Oe…

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Q: 3. Show by an example that the following statements are false. i. a - (b c) = (a - b) (a - c) for…

A: ( i )  a - (b • c) = ( a - b ) • (a - c )  fo all a , b , c belongs to real number R   We show that…

Q: If α = a (123456), show that a = (16)(15)(14)(13)(12).

A: A linear transformation is a function from one vector space to another that respects the underlying…

Q: 1 Evaluate dr. (포- 1)3/3

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Q: Fad the inverse f AB f 4. 5. and -1 AU

A: Given that , A-1=5-11-5 and B-1=-3-31-1 find inverse of AB.

Q: 13. Evaluate. ,zE (-x,0] 24 h(z) = zE (0, 8] (2– 1)(z+3) , z€ (8, x) h(-3) = [ %3D A. 27 B. 20 C.…

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Q: Find a fundemental set of solution vectors of the system x' = Ax where A is the given matrix: 2 -3 4…

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Q: A 21 2 B 22 스 23 C Z1 = 23 41+43 = 180° E 42+43 = 180°

A: We have to find the angle

Q: Q.10 If x = -1, then the value of x* is

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Q: Is there a better example of this... it's hard to follow

A: Let's solve.

Q: 22.2. From the following set of positive frequencies, obtain all other class frequencies. (A)= 23 N=…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.