(P(A U B) is . . P(A) U P(B X

Q: Find P(A U B), given that P(A) = 0.5. P(B) = 0.4, and A and B are mutually exclusive. 0.8 0.7 0.9…

A: We have given that P(A) = 0.5 P(B) = 0.4 Also, given that A and B are mutually exclusive

Q: The covariance between x and y is O 1.5 1.25 O 0.75 0.25

A: According to the given information, we have X Y 1 2 1 2 3 4 5 3 5 4

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

A:

Q: Find the nullity of T.T: P3→P1, rank(T) = 2

A: Here given

Q: If S is a subset of T , then u* ( T) sµ* (S).

A:

Q: Is the equation Bx = p consistent for all p in R^4? Explain.

A: Not consistent for all p in R4.

Q: 4. Assuming that the c possible subset of R (c) f(x) = V5 –

A: Use the definition of domain and range to solve this problem

Q: A. Let p(x) = 2x + 5x-3,m(x) = 2x- 1,and h(x) = Find: 1. (m-p)(x) 2. p(5)+ m(3)-h(1) +1 %3D x-2 3.…

A: A Given px=2x2+5x−3, mx=2x−1and hx=x+1x−2. 1 We have to find the m−px.…

Q: What are the ASSUMPTIONS for t?

A: A t-test can be used when the hypothesis is concerned with the population mean and the population…

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: Find c such that P(Z>c)= 0.3859

A:

Q: Suppose that SpyBorg Inc introduces a new computer game in Houston using television advertisements.…

A:

Q: -6 -3 0 3. [15p] А: and B Show that det A+det B ± det(A+B). 0 -12 1 9

A:

Q: Show that if E1 and E2 are measurable, then m(E U E2) + m(E1n E2) = m(E1) + m(E2).

A:

Q: {[(B U C)U A] N [(B UC)U A]}n {[(A U B)UC] nÃ}

A: We use the following properties of set operations: Distributive law: (A∩B)∪C=(A∪C)∩(B∪C)…

Q: Prove that (a) P(En F) = P(E)- P(En F) (b) P(EnF) =1-P(E) – P(F) + P(En F)

A: Solution: 6. Here, it is needed to prove that

Q: Let X = P(A) and E(3x) = E(2-6x) find A.

A: Solution: 46. From the given information, X follows Poisson distribution with parameter λ.

Q: 2. Suppose f: A → B and Y and Z are subsets of B. -1 (a) Will it always be true that f'(Yn Z) = f'…

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Q: Find the value of t so that t 4 -4| 2 3 3=4 4 5 0

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Q: z = ecos(2x)

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Q: If P(An B) = 0.3 find P(A U B°) O 1 0.3 0.7

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Q: In S, if T-{(G { G {), them r ) is In S, if T-1(G )G 2 3 \1 2 3 2 3 }, then 3 1 2 3 2 3

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Q: Let X P(A) and E(3x)= E(2– 6x) find a.

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Q: Q4/ Let S(x)=- x-1 S(x)= and g(x)=1+ Find (g(x) and ag)(x).

A: We define two functions: f(x) = x/(x - 1)  g(x) = 1 + 1/x = (x + 1)/x Then, we have to find the…

Q: P(−0.24°C<x<0.37°C)=P(−0.24<z<0.37)=

A: Solution: The probability which is needed to calculate is…

Q: The Direct Method of Formal proof 5. S → P P→ (W V J) SA¬W

A: To prove:            S→PP→W ∨ JS∧¬W∴ J

Q: For what a is ||ai - 3j + k||=16

A: Topic - vectors

Q: (a) Evaluate . z²e1/z where c is z = 1.

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

Q: Hint. You want to show |a| – |6| < |a – b| and -(lal – |b|) < la – bl.

A: Given: a and b are real numbers. To prove: a) a+b≤a+b b) a-b≤a-b

Q: If C is the constant of integation, and g(0) =1 the C=___ and g(-2) = ____

A:

Q: The covariance of X and Y is > 0, which of the following statement is a correct one? a. As X…

A: We have given the following statement about covariance.

Q: (r+ simo - coso)dr+r Csino tcoo + co-B

A:

Q: Which of the following is a possible y" + k'y = 0

A: Given that: y''+k2y=0

Q: 1. Let A = {x E Z | 6 divides x} and B = {x € Z | 3 divides x}. Prove that A C B, and then prove…

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Q: 1. Use Leibnitz theorem and find P3(x)? . v = (x+ 1)°u (x – 1)

A:

Q: Find the value of c such that E enc = 4 n = 0 3 1n 4 C =

A:

Q: Let X = {1,2,3}. (1 2 3 ) give a) For a (3 2 give a321

A:

Q: Let P= {p:p=6x-1, for some x EZ} and Q= {q:q=6y+5, for some y €Z}. Prove that P= Q

A: Answer

Q: A) If T (;) = () and T () = (). Find T((;) +2(^) +2(;) ( 5pts)

A:

Q: t, for t > 0, sa X 2 is

A:

Q: Suppose X~ N(u=120, o = 3), determine the value of x such that P(X>x) = 0.05.

A: Given that X follows N(mean = 120, SD = 3), then Z = (X - mean)/SD follows N(0,1)

Q: In P2 , if B = {1,1+x+x², x + 2} and D = {x²,x, 1} , then Pp-B = 1 2 0 1 1 1 1 0 1 0 1 1 1 1 2

A:

Q: p = irt, for t

A:

Q: Find the nullity of T.T: P5→P2, rank(T) = 3

A: Given T: P5→P2. The dimension of P5 is 6. T is a linear transformation from an n dimensional vector…

Q: Suppose p – a = 17. Find the following. %3D p + (- x) - (p – x) : * - p =

A: Given : p - x = 17

Q: 10 Prove that P(E U FU G) = P(E) P(F) + P(G) - P(E FG) P(EF€G) - P(EFG) - 2P(EFG)

A: Addition Rule of three events:For any three events E, F, and G, the addition rule states that:

Q: c) Evaluate ſ x*(In x)²dx

A:

Q: generally true? Prove / disprove this.

A: P(x+y|x)=probability of (x+y) given x. P(y|x)=probability of y given x.

Q: 3. Prove that (An B)² C A x B.

A:

Q: EF C and 0 are subsets of Y, then %3D

A: Solution for 6: Given C and D are the subset of Y. We have to show f-1(C)-f-(D)=f-1(C-D)

Q: [-8] Let v1 = 6 ,v2 =| 4 ,V3 = 8, and p =| 1 Determine if p is in Col A , where A= [v, v2 vz]. (a)…

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.