Find the joint CDF, F(t, s) for all t e R and s E R.

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: 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: If f-(a, b) = 0 and fy(a, b) = 0, then Vf(a, b) = 0.

A: Given,           fxa,b=0   and   fya,b=0

Q: 42x+10 b.4r nd rules for these t-tables: 10 47 6. 41 5. 21 22 100 405 10 31 2 2. 13 3. 17 100 497…

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Q: Prove the product rule by use of ΔA=w⋅Δh+h⋅Δw+Δw⋅Δh

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Q: (3, 4, 3) Let v = Calculate: vxi=( vxj=( v x k = ( A F ->

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Q: Let s = f(x, y, z) and x = = x(u, v, w), y = y(u, v, w), z = which of the following pieces of data…

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Q: Evaluate f (tcos² ti+1/tj+sec² tk) dt

A: To solve the following

Q: are linearly independent if and only if k # -0-2-0 v= -6 -1 + k 3 = 5 1 1 7

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Q: Let X and Y have the following joint probability density function: fx,y(x,y) = 1 / (x² y²), for x>1,…

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Q: Find fx and fy for f(x, y) = (1 - 2x + y)ex+2y Select one: a. None of these b. fx = c. fx (2 + x -…

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Q: determine L−1[F].

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Q: Evaluate f(х, у) ds. f(x, у) %3D у + 3 s: r(u, v) = ui + vj + 4vk, 0 sus 1, 0svs 4

A: Given: fx,y=y+3 S:ru,v=ui+vj+4vk, 0≤u≤1, 0≤v≤4 Differentiating r with respect to u, ru=1,0,0…

Q: Find f, and f, and evaluate each at the given point. f(x, y) = eXy2, (In 5, 2) fo(x, y) f,(x, v) =…

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Q: 1. Let f(x, y) = x + 2y. Find f (0, 1), f(2, -1), f(a, a), and f(a + h, b) - f(a, b).

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Q: 3. Find all functions from X = {a,b} to Y = {p,r, t}.

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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.