A = [2 -1 23 let it be.

Q: If i = 5+2, à = x - ỷ and b = j – z , show that a =

A:

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: Show that E[X]= a +V and o = b 4 4 -

A:

Q: If u (E) =0, then E is measurable.

A:

Q: EX.2.48: Nine people are going on a skiing trip in 3 cars that hold 2, 4, and 5 passengers,…

A: Total People = 9 Cars can hold 2, 4 and 5 passengers respectively Possibility of sharing the cars…

Q: Prove that the following relationship is true: nCr + nCr + 1 = n + 1Cr + 1

A:

Q: Let P = v?R/(R +r)² as in Example 8. Calculate dP/dr, assuming that r is variable and R is constant.

A: Given:

Q: Let ā = and b . Find 3ā + b. -

A: We will simply use vector addition rules to find the answer

Q: Let a2 + y2 + z2 = 3ryz, then which of the following is 一

A:

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: 9(r, t, г) — 5r(7 — сos(t)) — 82

A: We have to do partial differential here.

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

A:

Q: 2, 5x .3 b) Y = In 60(х, + + X, 2. 3.

A:

Q: Prove that ifx > 3 and y> 4, then xy > 11.

A:

Q: If (R – {0}, .) = (Q,.) then 1=0 1=-1 -1=0

A: For the given statement

Q: Let X and Y be defined as follows: X = {a E Z | a = 3x for some x E Z}, and Y = {b E Z |b = 3y – 3…

A:

Q: Given that =, = [3,0.7]. -2 = [2. 1.2] and =; = [4,-0.5]. (a) find xz, and z, x z3 (b) show that [1,…

A:

Q: If arg (z) < 0, then arg (-z) – arg * (z) equal to

A: Use the concept of arguments and representation of complex number in polar form.

Q: 4. If E(R) exists, show that |E(R)| < E(|R]).

A:

Q: ), then the value of r is

A:

Q: Let x e R,-1. Prove that VNEN (1+x)" >1+ nx

A:

Q: Suppose that A,B⊂S such that Pr[A|B]=25, Pr[A]=12 and Pr[B′]=12. What is Pr[B|A′]?

A:

Q: Prove if R(a) = (21 – A)*' +hen R(1)– R(µ) = (1H)R(2)R(µ)

A: Given that Rλ=λI-A-1 Let λI-A=Aλ                      . . . (1) So, Rλ=Aλ-1 ⇒I=RλAλ=AλRλ         . .…

Q: Find the of im < Re z< £ un der w-

A: Substitute w=u+iv and z=x+iy in the transformation. w=1zu+iv=1x+iyu+iv=x-iyx+iy.1x-iyu+iv=x-iyx2+y2…

Q: If i = j+z, i – j = đ, and j – z = b, show that ā = -15.

A:

Q: Show that e = o (hª) as h → 0 for all values of q.

A: Like big O notation, there is also a little o notation. There is a difference between big O and…

Q: Let A = {x ER : 2 < x < 3} and B = {r €R: -1 <r< 2}. Prove that |A| = |B|.

A:

Q: If (x+iy) = a+ ib, Prove that + a b = 4(a -b*).

A:

Q: Match these values of r with the accompanying​ scatterplots:: 0.371, 0.997. -0.71, -0.997, 0.71…

A: Given: r=0.371, 0.997, -0.71, -0.997, 0.71 We are asked to match these values with the accompanying…

Q: F(p), then prove that

A: simple use of integral transformation

Q: Let X~N (6,2) and P(X>a)= 0,3 Find a?

A: GivenX~N(6,2)Mean(μ)=6standard deviation(σ)=2

Q: Find the values of af /ax and af lay at the point (4, 5) if f(x,y)=x² + 3xy + y -1

A:

Q: If A is a 2 x 2 with det(A) = 3, then det(4A1) = %3D

A: det(A-1)=1det(A) det(4A-1)=4ndet(A-1) where n is the order of the matrix.

Q: If Ea, is divergent and 2b, is divergent, then E(a, + ba) is divergent.

A: Taking an example and than we are trying to understand tha statement.

Q: If c &gt;0, |u| &lt;c is equivalent to_______ &lt;u &lt;_______.

A:

Q: Let Find A = {x E R-1 ≤ x ≤ 4}, B = {x ER| 4 ≤ x ≤ 6), and C = {x E R/3 < x < 5}. AUC {-1, 2, 3, 4]…

A:

Q: Please asssit with value for ****,*****, ****** a

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: If C = {x:x² + 11x + 30 = 0, x ∈ N}, then C is a/an ?

A:

Q: Suppose A · B = 0. Show that this implies that C(B) is contained in Null(A).

A: Suppose A.B = 0 then we have to show that  Column space of B contained in the null space of A  i.e…

Q: Find (t), given 7(t) = (- 2 In(5t), - 5/5t, – et). %3D F'(t) =

A: Explanation of the solution is given below...

Q: Show that if A and B are similar, then AT and BT are similar.

A: Let A and B are similar matrices. By definition of the similar matrices.  The matric A and B are…

Q: Prove the followling identites 9) A-7-A 2. gn gntt

A: a) Given, ∆-∇=∆∇ Take LHS, ∆∇fx=∆∇fx Since, ∇fx=fx-fx-h ; Here h is the step size. and ∆fx=fx+h-fx

Q: Show that A ∩ B = A ∩ C need not imply B = C.

A: Let, A= {1,2,3} , B= {2,3,4} and C= {2,3,5}

Q: x, and x, in terms of t.) 2 1 -1 1 1 -1 1 2 1 2 2

A:

Q: = , where C is W 19

A:

Q: -x+y<y. 2 If x < y, prove that x <

A:

Q: Then prove that 3 (i) P (AUB) > 1 (ii) <P (An B) S 10

A: Answer: From the given data, P(A) = 3/5 and P(B) = 1/2

Q: a b be suc b |, then t

A:

Q: Let 1 A = 1 3 2, Find A- in terms of c.

A:

Statements and Logic

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