Let {Xr: r≥ 1} be independent and identically distributed with distribution function F satisfying F(y)< 1 for all y, and let Y(y) = min{k: Xky). Show that lim P(Y(y) ≤ EY(y)) = 1 -e¯¹. y→∞

Q: The faces x= 0, x= a of a finite slab are maintained at zero temperature. The initial distribution…

A:

Q: continuous function h(x),

A: Differential equation

Q: Calculate the divergence of cach of the following functions (a) r²î + y²§ + 2²k. (b) yzî + xzj+ xyk.…

A: As per the instruction, we will answer only the first 3 subparts. For (a), For a given vector fx, y,…

Q: Find h(x, y) = g(f(x, y)). h(x, y) = g(t) = t + In(t), f(x, y) = 4-xy 5+x²y² +In 4 - xy 5 + x²y² X…

A: Given: To Find: To find .To find the set of points at which  is continuous.

Q: If ƒ is continuous for a < x < b and differentiable for a < x < b , which of the following could be…

A: Here, given that f is continuous for a≤x≤b and differentiable for a&lt;x&lt;b.

Q: 1. For T € L(V,W), prove that null(T) = (range(T*)) and range(T) = (null(T*))+.

A: Given these, we can now prove the statements:  Proving (null(T)=(range(T∗))⊥):By definition, for any…

Q: 1. Let f(x) = x. Show that f is uniformly continuous on any finite closed interval [a, B] (Hint: x-y…

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Q: 4. Consider the Poisson's equation: Let u be a continuous and differentiable function in R, and let…

A: Let us start proving the problem step by step... Let us take f, g as two different variables which…