Prove that P(A) - P(3)| 4 P(AAB). where A is the symmetric difference.

Q: Q1-let A = 6a B - ; ) [2 3 & B = Verify that (AB)" = B" A"

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

Q: (2) |R| = |2N].

A:

Q: Then P(X > -2) is:

A: Here use givens probability distribution table for answer the question

Q: (b) Prove or disprove: Z10 ~ Z5 x Z₂.

A: We shall solve first question only as you have asked more than one unrelated question. For others…

Q: Q.2. Proof that V= u8--

A:

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: Did I prove p is not equal to 0 correctly? p is not equal to 0 by what?

A: You have proved correctly .   This can also be seen as If p= 0  Then 1/x = 0  and x= infinite or…

Q: diverges because an > 0. for all n 2 1. 2n + 1 True False

A: Given: The statement "an=n2n+1diverges because an>0 for all n≥1." To determine: Whether the given…

Q: 3. Prove that {12a + 4b |a, b e Z} = {4c\c € Z}.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Is the equation Ax = b consistent for all b in R^3? Explain.

A:

Q: 2. Using known theorems prove that P(ANB) > P(A) +P(B) - 1

A:

Q: Prove that AABC A DEF. C=2 E-4,2) 6-14.214 A 4) TF-.5)

A: Topic - transformation of a triangle Option 3 is correct Triangle ABC is translated by 8 units to…

Q: by xRy if and only if 7 divides x² – yʻ.

A: A relation is equivalence if it is reflexive,symmetric and transitive

Q: 3. By subtracting and applying Green's Theorem again, show that (gVf – fVg) · nds for-1 ef – fv°g)dA…

A:

Q: Q2/ Let X-N(4,9). Find (a) P(1 2). (c) P(|X2| >5)

A:

Q: What is t' (x) when t(x) = In( ): %3| 2x2+3x+2 Select the correct answer below: O t (x) = 2 + 4x+3…

A:

Q: What is the principal argument of z = 3 + V3i?

A: Let z=x+iy be a complex number. Then, the polar form of z is given by, z=rcosθ+isinθ where…

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

A:

Q: 7. Show that the equation p(x) = q(x)m(x) + R(x) is equiva- lent to the equation p(x) = m(x) + R(x)…

A: Given equation is  px=qxmx+Rx

Q: Va +3b + Va – 3b If x=- Va+36 – Va– 3b prove that 3bx² – 2ax +3b = 0 | - -

A:

Q: (b) Prove or disprove: f: 41o → Z20, [r|10 + + r2|20 is well defined.

A:

Q: Prove that 1 (c) 2F₁ (a, b; c; z)

A:

Q: inf f, is not measurable Vn. Isisn ulgn

A: False Statement

Q: ind the Wronskian of: 18x - 6 18x + 6 6x - 18 6x + 18 f₁ = x² - 6x f₂ = x² + 6x f3=x²-3

A:

Q: What is the sum of P(x) and Q(x) if P(x) = 4x2 + 6x - 9 and Q(x) = -7x- 12x +8? %3D 1. -3x2 - 18x -…

A: Given P(x) = 4x2 + 6x – 9 d(x) = -7x2 – 12x +8

Q: c. Find all the points X1 x2 in R3 [x3. that are transformed to Explain.

A: Given, the transform spantial coordinates                               x1x2x3into plane coordinate…

Q: 3) Find integers x and y such that 13x + 15y = 1.

A: We see, 15 - 13 = 2              => k(15 - 13) = 2k for any integer k              => 15 k -…

Q: iii) a) Prove that Pa(-x) (-1)".Pn(x) u (2n)! 22 (n!) b) Prove that P2n(0) = (-1)".- %3D

A: To prove- Pn(-x)=(-1)n.Pn(x)P2n(o)=(-1)n.(2n)!22n(n!)2

Q: 3. Which statement about k (z)= 3z -7z+2 is true?

A:

Q: a2 z a2z If z = In(x² + y²), find + 2 Əx2 ду?

A: The given function is z=ln(x2+y2).

Q: GIVEN: 2x - 3 = 7 PROVE: x = 5

A:

Q: (2) Determine k such kx? – 4x +÷= 0 that has real and different solutions. 2

A:

Q: (4x +16x² - 44X If-a) is the G.C.D. of ax² + bx+c and ex² + ax + b such that c 0, then prove a + b³…

A:

Q: Q2) If f(x) = (x), and g(x) = (2- x)i find (gof) (x) and the domain of (gof)(x).

A:

Q: Supppose that X ~ N (2; 3). Find P (1 < X < 4).

A:

Q: Let X~N(3,0²). Suppose that P(3<X<6)=0.4 · find P(X<0) ?

A: Given: X~N3, σ2 and P3&lt;X&lt;6=0.4.

Q: (b) Prove or disprove: f: 41o → Z20, [7]10 → [r2|20 is well defined.

A:

Q: B. Prove that (P- R) × (P + R) = 2(p × R)

A: We have to show that the given expression.  For this we will use the results of cross product

Q: b) Prove or disprove: Z10 ~ Z5 x Z₂.

A:

Q: Find the domain of gof, iff(x) =x² and g(x) = Vx-6. %3D O a.l-, - võJU(võ. x) O b. (-30, -6]U[6, ¤)…

A:

Q: Use the remainder theorem to determ a) (x2 – 7x) + (x + 5) :(x) + (x-1) :((-5)) + (l-5)-7) 1.5)…

A: By Remainder theorem :let  gx be the polynomial  and   a be any real number we can divide  gx by…

Q: use the convolution theorem to find L'{2+1 -1 4 Specifically s²(s²+1)

A: Given,        L-14s2s2+1=

Q: SHOW THAT P(x₂0) = 0.3₁ P(X=1) = 0.2₁ P(x7, 2) = 0

A:

Q: 3, 5x 60(x2 + *), 3 b) Y = In 7.

A:

Q: Let x € U = Q and p(x) : 3x² + 5x – 2 = 0. a. Write the following statement: (3r) p(x). b. Is it…

A: Given that: p(x):3x2+5x-2=0

Q: 4. Prove that n(3n – 1)r x + 4x + 7x + ... + (3п - 2)x for n e N.

A:

Q: Prove that V/3 (1-x) (1+2x) 33

A: To Determine :-  ∫01 x13 1- x 231 + 2x  dx  = 2π33

Q: {1 + x + x, x + x², for P2. Let >(x) = p(x)]B = 1 + 3x + 2x2. The

A: Here we have, B=1+x+x2, x+x2, x2  for P2. Let p(x)=1+3x+2x2 We have to find, p(x)B=?

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.