For events A, B, and C, we have the following probabilities: P(A) 0.7, P(B) = 0.5, P(C) = 0.3, P(A and B) = 0.3, P(A and C) = 0.1, P(B and C) = 0.1, P(A and B and C) = 0 = In the following, give your answers to two decimal places.

Q: In PCA, we obtain z E Rk from x E R" as follows: T z = u(1) y(2) u(k) Which of the following is a…

A: Given that,In PCA, we obtain z∈Rk from x∈Rn as follows:z=|u(1)| |u(2)| ...…

Q: Assume that P(A₁ N A₂ NA3) > 0. Prove that P(A₁ NA₂ NÃ3 Ñ A4) = P(A1)P(A2|A1₁)P(A3|A1 N A₂)P(A4|A₁…

A: We have conditional probabilitiesP() =       (i)P( =                       (ii)P( =…

Q: 7. Given P(A) = 1/3 and P(B) = 1/2 and P(A U B) = 2/3 . • (a) Find P(A¹) . . (b) Find P(A and B) (c)…

A: Given data, p(A) =13p(B)=12p(A∪B)= 23we have to find out the given probabilities.

Q: What is the relative risk for the association between men and women vs COVID-19 infection? What do…

A: Data is given for Men and women, vs Covid infection ( Covid positive and Covid negative We have to…

Q: If Var(X1) = 2, Var(X2) = 4, Var(X3) = 3, Cov(X1, X2) = 1, Cov(X1, X3) = -2, and X2 and X3 are…

A: Solution

Q: 1. Suppose P(A) = 4/10, P(B) = 5/10, and P(AB) = 2/10. (a) Compute P(AC). (b) Compute P(AUB). (c)…

A: As per our guidelines we are suppose to answer only three sub parts.…

Q: (8-j8) x + (3-j2 ) y + (7 - j9 ) z = -9 + j7 ( -4 - j7 ) x + ( 1 - j1 ) y + ( -2 - j4) z = 9 - j6 (…

A: This is a problem of linear transformation.

Q: P(A)=0.02 and p(C)=0.07 determine p(A u C), given that A and C are independent

A: It is given that:And, A and C are independent events.

Q: Let x be the number of teachers among 3 people selected randomly from a group  consisting of 3…

A: Probability: Probability is the ratio of favourable outcomes to all other potential outcomes of an…

Q: Compute using Lagrange Inerpolation f(-0.016) for the data (-1.5, - 14.1014), (-0.75, - 0.931596),…

A:

Q: (b) Let X = {A E Mat2(R) : A is upper triangular} and let Y = {A € Mat2(R) : A is lower triangular}.…

A:

Q: 6. (10pts) Determine whether you can find the interpolating polynomial p(t) = a, + a,t + a,r² for…

A:

Q: SupposethatAandBaretwoindependenteventswithP(A) = 0.3andP(B) = 0.3. Calculate(a) P(A and B) (b) P(A…

A:

Q: P(ANB) = P(A)NP(B).

A:

Q: Find (a) ||u||, (b) ||v||, (c) u ∙ v, and (d) d(u, v).u = (1, 4), v = (2, 1)

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: Let a : V → W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2,…

A:

Q: Consider the following simple linear regression. Y = Bo + B₁X + e, ed N (0,0²), i=1,..., n.

A: is a random variable: represents the dependent variable or the response variable in the regression…

Q: p(+) = + = Find P (Q(+) P(Q(r) Q (t)=1 ++1

A:

Q: 4xdx Evaluate J ax+41

A: Here I am attaching image so that you understand each and every step.