Let α and β be positive integers and X ~ Geo(p). Show that P(X > α + β | X > α) = P(X > β) = qβ

Q: Let X and Y be independent, and let X be N(10, 1) and Y be N(11, 1). PIX >Y),

A: From the given information, X and Y are independent random variables. Let X be a N(10, 1) variable…

Q: If zis implicitly defined as a function of x and y by xy-yz+xz=0, find dz/dx. (y+z)/(y-x)…

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Q: A fair coin is tossed two times independently. Let H₁ = {1₁ (1, if head is obtained at the ith toss…

A: When head is obtained at 1st toss then H1= 1  When head is not obtained at 1st toss then  H1= 0 When…

Q: x and y are independent and uniform in the interval (0, a). Find the p.d.f. of (a) x/y, (b) y/(x+y),…

A: The objective of the question is to find the probability density function (pdf) of three different…

Q: Let f(x) = 2x + x2 on [0,7]. Let p ={0,3,4,7}. Let a(x) = 2x2 on [0,7]. Give the numerical value of…

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Q: Let X~N(10,9). Find P(Z > -2)

A: It is given that, X~N(10,9)

Q: Į c(x + y?) for 0 <x< l and 0 < y < 1, S(x, y) = otherwise. Determine (a) the conditional p.d.f. of…

A: The required pdf is given by: fy=∫01fx,ydx=∫01cx+y2dx=c∫01xdx+∫01y2dx=cx22+xy201=c12+y2

Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: Let Find A = x³y 1-2xz] + 2yz k Vx(VxA).

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Q: (b)* Show that Y' is closed.

A: Actually we shall show, closure of the set = the set. Then this set will be closed.

Q: . Find div(F x G) = V · (F × G). F(x, y, z) = i + 9xj + 3yk G(x, y, z) = xi - yj + zk div(F x G) =

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: - Find V x+y `

A: Given that, fx,y=x+yx-y We have to find ∇f. We know that, ∇f=∇x+yx-y=∂f∂x,∂f∂y

Q: Compute Au, where A Au = = 1 (56) 4 and u= (9).

A: The simple matrix product..

Q: find an antiderivative Fon of the function fox)=5sinX such that FCO)=1.

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Q: Find V x (V x F) if F(x, y, z) = 5xyj+ 9xyz k. V × (V × F)

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Q: aF O F2 aF, If F = F,I+Fj +F,k then prove that div F = + ду

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Q: Let r = xi + yj + zk and r = |rl. If F = find div(F). (Enter your answer in terms of r and p.) p'…

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

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Q: Let \n (xy) + y ² = x6+3 find dy ax

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Q: Suppose that P(A') = 0.3, P(B) = 0.8, P(A U B) = 0.9. Find P(A), P(An B), P(An B') and P(A'|B).

A: We have given that P(B) = 0.8 We have to find P(A),  and

Q: Let X ~ Exp(λ). Find F(X) and E(X).

A: Let X ~ Exp(λ)The probability density function of X is fx(x)=e-λx   ;x&gt;0

Q: Let X=(1,0, – 1,-V2)'. Then, ||X||2 = Select one: а. 3 O b. 4 C. 2 O d. 1

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x :x > 5}. Find h. D'n (AUB)

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Q: Let f(x, y) : = x/Y Evaluate f(3, 4)

A: We need to evaluate f(3,4) To evaluate we need to plug in 3 for x  and 4 for y

Q: Let f(x, y) = e"r³ Evaluate f(3, 0)

A: The function of two variables  x and y will be of the form,   The function value of this kind of…

Q: Let (a,m) 1 with m>1 and let f = expm (a). Then

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Q: Let f(x) = 2x + x² on [0,7]. Let o = {0,3,4, 7}. Let a(x) = 2x² on [0,7]. Give the numerical value…

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Q: Find дz əx 2 x²y²exy for zx

A: Let's find partial derivative.