1. Let Z defined by the product of two numbers taken separately from two boxes containing 1, 2,3 and 4.

Q: 29. Compute det B, where B = 1 2 2

A:

Q: 1) Evaluate whether y, and y, are uncorrelated 2) Evaluate whether y, and y, are independent

A: Given, y1y2 = 111-1x1x2 So,  y1 = x1+x2y2 = x1-x2 And, Mean is 0 and Variance is 1 So, E(xi) =0…

Q: 6. Prove that if gcd(a , b) = 1, then gcd(a + b, ab) = 1.

A: We need to prove that if gcda,b=1 then gcda+b,ab=1 Let us on the contrary assume that  gcda+b,ab=c…

Q: If (0,1) ~ (-1,1) and (-1,1) ~ R. Deduce that (0,1) ~R

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Q: 2 Let A | and U = H. Then A2017U is equal to = ... A) B

A:

Q: ΔXYZ, XY = 6.32, YZ = 5.83, and XZ = 11.05. m<y= (blank) 25.6 degrees 85.1 degrees 113.4 degrees…

A: Given query is to find the the measure of angle y.

Q: Show that for n, m e Z+, gcd(2" – 1,2 – 1) = 28cd(n,m) – 1.

A: To prove : gcd(2n-1, 2m-1)=2gcd(n,m)-1where n,m ∈ℤ+

Q: 1. If = (1,0,-3) and i= (6,-3, -4) compute ixw.

A:

Q: Let C: z-3 and I – 6dz. ONone of these

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Q: If A= then A" + nl is equal to

A:

Q: 4- Suppose that A = {x1 = (2,0,1), x2 = (1,–1,4), x3 = (-1,–2,1)} and B = {y, = (-1,0,2), y2 %3D %3D…

A:

Q: 2. Find all number z such that Az" + Bz² + Cz = D a. A= 2

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a ·…

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Q: 2.4.3. Let p(r1, T2) = 16, T1 = 1, 2, 3, 4, and r2 joint pmf of X1 and X2. Show that X1 and X2 are…

A:

Q: Let x, y, z, w ∈ Z and n be a positive integer. Suppose that x ≡n y and z ≡n w. Show that x + z ≡n y…

A: Suppose that x ≡n y and z ≡n w then, (i) we are assumed that  x-y=k1 n  and  z-w=k2 n  for some…

Q: 4 Show that a + B = B +a for all a, BE C.

A: We can write alpha and Beta in general form of element of complex number.

Q: Show that z, + z, = =, + 2 .

A: We have to prove that z1+z2=z1+z2 Conjugation: Let z=x+iy be a complex number. Then, the complex…

Q: 3 10. Show that R² span

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Q: 4. Consider a problem 7 defined as; T: Given a set of n positive integers A = {a1, a2, · ·· , an},…

A: To display that any difficulty A is NP- complete, 4 matters are critical to be appeared. The first…

Q: (c) Show that a permutation o E S, commutes with r if and only if the permu- tation f(o) commutes…

A:

Q: Prop (1.23 ≤ x ≤ 1.72) = Prop (-2.50 ≤ x ≤ 0.5) = Prop (x ≥ 3.00)

A: here use normal distribution table

Q: Prove that d24 and s4 are not isomorphic. List elements and there order.

A:

Q: 2. Find three positive integers x, y, and z if their product is 27 and the sum is a minimum.

A: Given three positive numbers are  x, y, and z Product = xyz = 27 And sum is minimum

Q: Prove that if n> m - 1, then J,(x) = 2(x/2)"-m

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Q: *prove that for . P+2+3+... +n° = 2 n=!,2,3,

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Q: Shaa thut the graf of lincs iju fins rom F from E Iwhore is a iomasphic wilh Ge(5)

A:

Q: 3. Show that if A-1 exists, then eAT dr = A-1(eAt – I) = (eAt – I)A-1.

A:

Q: Suppose A1, A2, ..., 430 are thirty sets each having 5 elements and B₁, B2, ..., B₁ are n sets each…

A:

Q: 10. Prove that Z has no smallest element.

A: we will prove it by contradiction, Suppose x belongs to Z  is the smallest element.

Q: Let V = {cities of Metro Manila} and E = {(x, y) |x and y are adjacent cities in Metro Manila}. %3!

A: Given: Let v= cities of Metro Manila  and E=x,y/ x and y adjacent cities in Metro Manila The…

Q: [2 Compute: 1 4 2 - . Preview

A: Solving the problem by finding the the multiplication of the given matrices.

Q: Prove that if A is similar to B and B is similar to C, then A is similar to C.

A:

Q: Let a = (1, 3, 8) and b = (7, 3, 4). Compute 5a + 7b

A:

Q: 2. What is the largest possible c in (1) if X=R² and x₁=(1,0), x₂ = (0, 1)? If X = R³ and x₁ = (1,…

A: Given: c To find: a) X=R2b) X=R3

Q: 1. Compute n, μ, EX, and EX² 5, 7, 3, 4, 1 2. Compute n, EX, (EX)², and EX² X 7 5 6 2 3 f 2 3 4 2 1…

A: 1) n x x^2 1 5 25 2 7 49 3 3 9 4 4 16 5 1 1 sum 20 100 n=5 μ = ∑xn = 205 = 4 ∑x =…

Q: There are two food carts serving food at a local park. At any given time, Let A denote the number of…

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

Q: Show that For all z € C, with z + 0, then: |z|?z=1 = z

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Q: Compute det B4 where B

A:

Q: Show that If |z| = 1, then: -1 = Z

A: z is a complex number. z=a+ib |z|=(a+ib)(a-ib)     =a2-b2 if |z|=1, then a2+b2=1

Q: 1. Compute n, μ, EX, and EX² 5, 7, 3, 4, 1 2. Compute n, EX, (EX)², and EX² X 7 6 5 4 3 2 1 f 3 2 1…

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Q: Let a,b,c be intergers with gcd(a,b)=1 and c|(a+b) (c divides a+b). Prove that gcd(a,c)=1 and…

A:

Q: Compute 0.5x for the following set of n = 7 values. x1 = 4, x2 = 19, x3 = 18, x4 = 10, x5 = 16, x6 =…

A: Solution: From the given information, n=7 and the set of values are

Q: Compute SS, SP, and r.

A:

Q: 3. Show that if (AB)₁, (αB)₁, (Aß)₁, (αß)., and (AB)2, (αB)2, (AB)2, (aß)2, be two aggregates…

A:

Q: In Z, let H = &lt;5&gt; and K = &lt;7&gt;. Prove that Z = HK. Does Z = H X K?

A: Given: In Z H=5K=7

Q: Let z, =1-1, z, =-2+4/, and z, = 3-21. Find Im().

A: Multiply z1 and z2 then divide by z3 then solve and get imaginary part

Q: Let S = {2x, 1 – x, x² + x – 1,x + 1,x – 2}. Then %3D P3 P2

A:

Q: Let n=23 and consider the following information, Model One: Y = Bo + B1X1 + B2X2 + B3X3 + B,X4 +e…

A: Solution: Given information: n= 23 observation: k= 3 independent variable  R2=0.8685

Q: Compute d(ū, ū), d(ū, w) and d(ū, w) where ū, ū and w are

A: Given: u¯=12-48, v¯=8-241 and w¯=2-418 To find: du¯, v¯, du¯, w¯ and dv¯, w¯ where d is distance…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!