P(0) = {0} P(A) \ {0} P(A) ACB iff P(A) CP(B).

Q: E [X - E ( X)]2 is Select one: O a. V( X) O b. E ( X) O c.E ( X2) O d. S. D(X)

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Q: IT X) IS defined as foilows, ina (a) i( – 2), (D) (U), and (C) I(2). x? if x 0 (Simplify your…

A: Since the given function is a piecewise function therefore we need to take care of the branch of the…

Q: the second

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Q: If F(n) = Σo(d) then F(175) d|n

A: What is Sum of Divisors: For a positive integer n>1, the fundamental theorem of arithmetic shows…

Q: The residue of f(2)=- (A) 1 2011! 1 (B) 2010! (C) 2010! 1 (D) 2009! 2011 at=0 is

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Q: 8-3 (IB) The value of linn is 3r21 (A) - (B) 등 (C) 0 (D) 6. (E) DNE (F) O E OF Oc OD 17

A: Solve limit

Q: Find f(t). f(t) = कर 2 1 4s+5

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Q: Let X b(n,-) and E(x) = E(2– 6x) find n.

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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: Given that P(X)= P(Y)= and P(XUY)= find 20 20 10 a) P(XnY) b) P(XIY)

A: Given,PX=920PY=720and PX∪Y=710

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Let r(t) = the number of road-runners in year t, and let c(t) the number of coyotes in year t. Then…

A: The objective of the question is to find the values of r(1) and c(1) for different initial…

Q: * Find the derivative lic F (+) = (+³-2+ +1) (2+²

A: Given query is to find the derivative of the expression.

Q: Find f(t). &{ 4s - 1 3 \s² (s + 1)³√ f(t) = 7H(t)-t-7e --(61-5-12) 6t- - e X

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Q: (d) Fact (i): It can be shown using part (c) that Fact (ii): It can further be shown using Fact (i)…

A: Given, p,q:[0,1]→R are three differentiable functions. Also p'''(x)=p(x) and q'''(x)=q(x) for all x…

Q: Let P(E)=0.85, P(F) = 0.23, and P(EUF) = 0.94. Find (a) P(EIF) and (b) P(FIE). (a) P(EIF) = (Type an…

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Q: P (X=(X+X/3 ), for x = 0,1,2 3 4 find what's to come P(x 2 3) P[( x=3) U(x=4)]• P(x=3) + P (x=4)•

A: Given P(X) = 1D(X + X/3)  ,  for  x = 0, 1, 2, 3, 4

Q: If n = 17640 then find (n)

A: Given: The given value of n is 1640. To find: The Möbius Mu Function of a given number. That is to…

Q: Iff (x) = Vx ;g(x) = x +1 find a.(f og)(x) b.(g o f )(x) c.(f of)(x) d.(g og)(x)

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Q: Let p(x) = 5x² – 3x + 2 and suppose that y 1 0 A = |0 1 0 0 y for some y E R. Evaluate p(A).

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Q: (7) Let X P(a) and E(x)= E(5-5x), then 2 is. (a) 25/26 (b) 26/25 (c) 12/26 (d) 26 (e) None of these

A: We know that the if X~P(λ), then E(X) =λ

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

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Q: Find S T(1– a²)+ 5* + 5m(1+ a²)| dæ.

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Q: Find F(0) if F (t) == L-! 16 82 (s+4) O 16 O 4 O 2

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Q: Let G = (Zio, X10) then o(G) is (A) 2 (B) 4 (C) 5 (D) 10

A: If G is group then it satisfied closure law

Q: Ext (A) n Bd (A) + Ø True False

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Q: Let r(t) = (a) Find 7 (t). (b) Find Ñ (t). (c) Find K (t)

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Q: Find P(C/A) and P(C) if p(A1) = 0.6 B1 0.8 0.7 C1 A1 C2 A2 0.7 B2 0.8 %3D [Hint: P(C/A) =…

A: Probability mass function P(X=xi) Simple facts about pmf  ∑(X=xi) =1iP(X=xi ∩ X=xj)=0 if i≠jP(X=xi ∪…

Q: 10 F(s) s(s + 1)(s² + 8s + 15)

A: Given Fs=10ss+1s2+8s+15

Q: Prove that: ^ ( a ) 2 ² 1 ( ² + ²; ; ; ; ; x ² ) = ↓ sin¯' x } 3 + 2² (¹-²)=an (b) 1 ¹ tan^¹ x ܐ

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Q: Let f(x) = (3/2)x2, −1 1/2). (b) Find P(X2 > 1/2). (c) Find P(|X − 1/2| < 1/4). (d) Find the CDF…

A: We have given the following pdf

Q: A(X) = 1 1 1 1 1 1 € Rnxn det A(A) = (A-1)-¹(X+n-1).

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Q: Find (x + 2)(x-7)dx (x + 2)(x − 7)dx= + C

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Q: Consider the following. P(A) = 0.27 and P(B) = 0.45, and P(A and B) = 0.1215 (a) What is P(A | B)?…

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