Assume that Pr[E]=0.5Pr[E]=0.5, Pr[F]=0.65Pr[F]=0.65, Pr[G]=0.45Pr[G]=0.45, Pr[E∩F]=0.35Pr[E∩F]=0.35, Pr[E∩G]=0.15Pr[E∩G]=0.15, and Pr[F∩G]=0.35Pr[F∩G]=0.35. Find the following probabilities: (1) Pr[E∪F]=Pr[E∪F]=  (2) Pr[F′∩G]=Pr[F′∩G]= (3) Pr[E′∩G′]=Pr[E′∩G′]=

Q: assume that Pr[A′]=0.55, Pr[B]=0.35 , and Pr[A′∩B]=0.2. (1) Pr[A∩B]=Pr[A∩B]=   (2)…

A: Solution : Given information; P(A')=0.55 P(A)=1-P(A')=0.45P(B)=0.35 and P(A'∩B)=0.2

Q: Prove the shifting theorem F[s(t + to)](w) = exp(+iw to) F[s(t)](w).

A: The Fourier Transformation of a function is given by;,   where The objective is to prove the…

Q: Let S be a linear transformation from R³ to R2 with associated matrix Let T be a linear…

A:

Q: Let f and g in F[x] be non zero elements. (a) deg(fg) = deg(f) + deg(g) (b) f is a unit iff deg(f) =…

A: For the solution of the problem follow the next steps.

Q: Suppose P[X] = 0.4, P[Y ] = 0.27, and P[X ∪ Y ] = 0.52. Find P[Y | XC]. Where XC means the…

A:

Q: Give an interval over which the set of two functions fi(x) = x² and f2(x) = x |x| is linearly…

A: Given: The set of two function.f1(x)=x2f2(x)=xx

Q: Give an example where | f(x)dg(x) exist even through f is unbounded on [a, b].

A:

Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: Suppose that A,B⊂S such that Pr[A|B]=3/7, Pr[A]=3/10 and Pr[B′]=13/20. What is Pr[B|A′]? Write as a…

A:

Q: Let u = and v=. (a) Find ||u||. (b) Find u – 3v. -

A: Given: u=1,4,3  and v=2,0,-1

Q: Evaluate f (x + y - z)² dV for the box B with dimension: [0, 8] × [0, 7] × [0, 3]. B (Use symbolic…

A:

Q: Let fx (x) = x +b, x ∈ [−2b, 2b]. For which b is fX (x) a pdf?

A: Given,  fx (x) = x +b, x ∈ [−2b, 2b] To find the value of b for which fX (x) is a pdf.

Q: Find real numbers x, y and z such that (x + 4)i + (y – 5)j + (z – 1)k = 0

A: To Determine :-  The real numbers x , y and z  such that   x + 4  i +  y -5  j +  z - 1  k =0

Q: Let Pr[A]=0.6, Pr[B]=0.7, and Pr[A u B]=0.8  find Pr[A/B]

A: From the provided information, Pr[A] = 0.6, Pr[B] = 0.7 and Pr[A Ս B] = 0.8

Q: Let f : Z+ → N be the floor function f(x) = [(x – 1)/2].

A:

Q: Find ||F||. F(x, y, z) = i + j + k

A:

Q: g is a coordinate system for a line L and a ∈ R, then the function f : L → R given by    f(P) =…

A:

Q: Prove that P[X |Y ] = (P[Y | X] · P[X] ) / P[Y]

A: From the definition of conditional probability, for two events X when Y is given PX|Y=PX∩YPY

Q: Let f(x) = |x|+|x−2], x € R. Find points where f is not differentiable.

A:

Q: Find the (natural) domain of the function x + 1 2х — 1 f (x) = Select one: a. (-0, –1] U (1/2, ∞) b.…

A:

Q: If x has a value of -4, determine if the series converges (absolutely or conditionally) or…

A:

Q: Determine U(Z[x]).

A:

Q: Assume that Pr[E]=0.65Pr[E]=0.65, Pr[F]=0.35Pr[F]=0.35, Pr[G]=0.6Pr[G]=0.6,…

A: Given:

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: C) Find S x²e¬x dx

A: Integration by parts formula:

Q: Consider the function f : R³ → R defined as V(x1, x2, x3) E R³ f(x1, x2, X3) = X1X2+ X1X3 + X2X3 a.…

A: We are given the function f: ℝ3→ℝ defined as ∀x1, x2, x3∈ℝ3    fx1, x2, x3=x1x2+x1x3+x2x3. For (a),…

Q: Encik Samsudin, a PhD student has reported the concentration of E.coli bacteria, C(μg/L) in a…

A: Given: C=kmaxt25+2t2+3.5t To find the root and to determine the fastest time for the E.coli…

Q: Evaluate f (x + y − z)² dV for the box B with dimension: [0, 6] × [0, 4] × [0, 3]. (Use symbolic…

A: Solution :-

Q: Consider the function ƒ : R → R defined by 2x + 5, ax² + x, Show that there is a value of a for…

A:

Q: Suppose that Pr[A]=8/13, Pr[A|B]=5/7, and Pr[B|A]=5/8. Find Pr[A′|B′]

A:

Q: Find all functions f:R → R that satisfy the equality xf(y) + yf (x) = (x+ y)f(x)f(y) %3D for all r,…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.