9. For n = 1,.., n, let X, be independent r.v.'s such that P(X,=1)= p,, P(X,=0)=1-P,- %3D Under what conditions on the p, 's, X- >0, as n→ 0.

Q: 6x2+7y2=C satisfies 6x+7yy' given the inital condition y=4 when x=6 what is C.

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Q: Let X=(1,0, – 1, -/2)'. Then, ||X||=v2 Select one: True False

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Q: 3. Let f be continuous on [-1, 4] and differentiable on (-1,4). If f(-1) = –1 and f(4) = 4, then the…

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Q: 1. (J · K) v (~ J. ~ K) / :. J = K

A: There are three expression in the given logical statement. They are J.K ~J.~K J≡K We prove the two…

Q: Find f. f '(t) = 4 cos(t) + sec2(t), -r/2 < t < t/2, f(T/3) = 4 TC + tan 3 +4 -3/3 3 TC f(t) = 4 sin…

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Q: 5. Let U ~ U[5, 10] and let X = I5,7) (U) be the indicator function of [5, 7) and let X,…

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: 2.x²y"+xy'–3y= 0,x>0

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Q: U Tangent prom (0-1) to y² = n³ passes through (4,8) (1,-1) (1,1) (3,4) A₁

A: The curve is  and the point is

Q: 5. f'(x) does not exist for x = А. 1 only B. 1 and 2 C. 2 and 6 D. 0,1,2, and 6

A: Note f'(x) of constant is 0 always

Q: Let U1, U2, U3, .,U48 be independent and identically distributed U,~Unif(0,1) and X = U, + U2 + U3 +…

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Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: Show that 6.8) fdx + gdy = Jc.8) (12,16) • (12,16) - (28x³3 By³dx + 35ytx dy) is independent of…

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Q: (1).p^((Vq)^-p) → q); (2). ¬(p →(pVg))^r.

A: WFF is a well formed formula. There are three types of wffs: Atomic formula: A predictable symbol…

Q: Suppose X~U(a, b), with µ = 1 and ² =. Find P[X < 0]

A: Solution-: Suppose, X→U(a,b), with μ=1  and  σ2=4/3 We want to find P(X&lt;0)=?

Q: what is the averaage value of y=a/x on [1,b]?

A: First we have to find formula of average value.

Q: 14. If f(5) = 19 and f'(x) 2 3 for 1 <x < 5, then f(1) is at most: %3D A) 3. B) 4. C) 5. D) 7.

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Q: let p(x)=g(f(x)). use the given table to find p'4

A: p(x)=g[f(x)] diff. w. r. to x p'(x)=g'[f(x)] . f'(x)  ..................(1)

Q: If f =x-e" and F=x'yi-2y'zj + xy'z'k, find: div(F x grad(yf )) at (4,1,-2)

A: The function                     Then, we have to find

Q: 29. Show that the functions (x) = sin mx, m = 1, 2,... are orthogonal over the interval [-, ].…

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Q: , for x 1 Let f(x) be a function de fined by f(x)3= Discuss the contuniuty of f andf".

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Q: 2(x-1) If y = Vx² – 2x then y' 3x2-2x

A: For the first part, we differentiate the given function y with respect to 'x' and use change rule of…

Q: 2.2 11, IfF = xyz\+x*y°z}+ xyz k then find div F at (2, 1, – 3).

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Q: of Let f(x,y)=tanh-1(x-y) with x=e" and y= usinh (1). Then the value of Ot (u,t) =(4,In 2) is equal…

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Q: Je fine a binary relation Rond by R= [(y)] ER² x ус

A: Given is : R={(x,y)}∈R2:x-y∈Q We have to show that it is an equivalence relation.

Q: Find the value of f(-1) when ƒ"(t) = 6(2t − 1) and ƒ'(1) = 6, ƒ(1) = 1.

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Q: Salve it passible mehad (a) of 2 separalian A variabld Uxx= cur ul0,t)= 0, uct) = To+ %3D ulu,0) (2)

A: According to our company policy, I am supposed to answer only one question at a time. For the rest…

Q: A clamped spline S for a function f is defined on [0, 2] by S(x) = S0(x) = 3 − 2x + ax^2 + 2x^3 , 0…

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Q: 7. Modify B(3) to construct a C* function C(2) which satisfies C(2) = 0 if z S 0.. a. b. C(z) = 1 if…

A: please see the next step for solution

Q: =Xtanx dk, Prove that ="IH (n+1)I,+(n-1) -1 T 1 2 n

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Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

A:

Q: 13. Use a u-substitution to evaluate /x²/(x³ – 2) dx

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.