1. Let P(A) = 0.4 and P(AUB) = 0.6. For what value of P(B) are A and B independent?

Q: For a population with u=90 and o=20, a score of x=105 would correspond to a z-score of

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Q: 10. dr S f(æ) dx = Choose...

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Q: 6.8 Obtain a test for Ho: B1 = c versL

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Q: Show that E[X]= a +V and o = b 4 4 -

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Q: 16) Use the given diagram to calculate P[(A U B)| C) A. 0.2500 B. 0.4127 C. 0.0848 0,25 0.02 0.01…

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Q: S(c^~q) S→(-avr) a p

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Q: Let P = v?R/(R +r)² as in Example 8. Calculate dP/dr, assuming that r is variable and R is constant.

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Q: Solve the following first-order linear DE's. y' + (cotx)y = xcscx, yE) = 1

A: Two ways it can be solved. 1)By making exact form 2)Using integrating factor

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Q: Let a e R" and let A = aaT. Show that xT Ax = (a" x)².

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Q: 4. Explain why (* + ÿ) + (ž + t) equals MQ in the following diagram.

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Q: АРТЕ -> Z. K E. P.

A: Given : 2 parallelograms of the same size

Q: 3 - find " if w z 4 e Lny and X = hn(ucosul y = = Usinv = usinu , cu v) = (2,) cugv) = (2,

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Q: 3. How would you classify AG? A J G

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Q: 4. If E(R) exists, show that |E(R)| < E(|R]).

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Q: (d) Are X1 and X2 independent? Justify. (e) Compute E(X1) and V(X1).

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Q: Suppose that X and Y are unknowns with E ( X ) =12 and E ( Y ) =20.  If E ( XY ) =225, then what is…

A: E(X) = 12 E(Y) = 20 E(XY) = 225

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

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Q: 2. Given s(x) = (1- ,0 <x< 100, 100 Calculate p(36) and E[T(36)].

A: Given information: s(x)=1-x100, 0≤x≤100

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A: We will prove what relationship these two triangles have.

Q: (10) If H < Z» × S, with |H| = 12, then H = %3D

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Q: Let X~N (6,2) and P(X>a)= 0,3 Find a?

A: GivenX~N(6,2)Mean(μ)=6standard deviation(σ)=2

Q: two variables are independent, each with the pmf given in the accompanying table (so X,

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Q: Suppose E(X)=2, E(Y)=4, E(Z)=10. X, Y, Z are dependent. What is E(2X+3Y+Z)? Can not compute with…

A: Given,E(X)=2E(Y)=4E(Z)=10X,Y ,Z are dependent

Q: 6. Find Ar for A = and z= Az =

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Q: Suppose that  X  and  Y  are unknowns with  E ( X ) = 12 and E ( Y ) = 20.  If E ( X Y ) = 225,…

A: It is given that, E(X) = 12, E(Y) = 20 and E(X,Y) = 225.

Q: LetS 2 x;-x)2 be a biased estimator foro, then the bias= ni= 1 Select one: a. -D1 b. in d. 1 1/n

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Q: 2. Let P:C0, 1] → C|0, 1] be given by Pp = " – e°. Compute dP(y). Be sure to justify your…

A: We have Pφ=φ''-eφ We need to find dPφ If we have  y=fx⇒dydx=f'x⇒dy=f'x dx Similarly, we find dPφ for…

Q: d. What happens if P < M for all t?

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Q: If z = x – 3y, then w = 2 Using the calculation above, mark the s

A: Linear span: Let V represent a vector space, and S=v1,v2,...,vn represent a subset of V. If every…

Q: Suppose C varies interversely as/ with m^2, and C=72 when m=4. Find C when M=12.

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Q: If s=5√t+4, then ds/dt =

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Q: 3) If X ~ N(5,2). Calculate P(200<Eº,x;<300) = ?. Draw a figure. '

A: Given : X~Nμ=5,σ2=2 Let, if X~N(μ,σ2), then ∑i=1nXi~N(nμ,nσ2) For n = 50…

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

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Q: Let P(A) = 0.4 "and " P(AU B) = 0.6. For what value of P(B) are A "and " B are independent?

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Q: 43. fry(x, y) if = e"* f(x. y) en?

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Q: - [o• P + 4)[5(t) + 48(t – 2)]dt. a) I b) I = P[8(t) + 8(t + 2.5) + 8(t – 5)]dt.

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Q: a) Is it reasonable to assume X; and Y; are independent? b) Is it reasonable to assume X; is…

A: According to the answering guidelines,  we can answer only three subparts of a question and the rest…

Q: Given N=10, Σr 140, Σy - 150, Σ(-10)--180 %3D Σύ-15- 215, Σα-10) -15) 60 h to %3D ad K.P.…

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Q: he joint pmf of X and Y is given below. What is E()XI-M)? Y -1 1 X 1/16 1/16 1/16 1/8 1/16 1/8 1/8…

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Q: Let z=xin(x2+y²-eª)-162xy, x=te°, y=et. If the value of when s=2 and t=1 is equal to Ae?+Be", then…

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Q: let fho=3*-1지 , t E=(12] 州 fefE)?

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Q: Suppose that X ~ Unif(-1,1). Compute (d) P(X = 0.5), (e) P(X² > 0.5).

A: Let ,  The pdf of X is ,  = 0 ; otherwise Our aim is to find the following :  d) P(X=0.5) e)…

Q: Q/ Consider the following four points to interpolate for y = f(3.2) using: X 1.0 0.1111 2.0 0.0625…

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Q: S that is closest to b.

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