Let {X} be i.i.d. such that X₁~ Pa(4, 1500) and suppose that N(2) ~ Po(100). Find E[S(4)] and Var[S(4)].

Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: Find f(x) and g(x) such that h(x) = (f o g)(x). Let g(x) = 2x + 1. 3 h(x) = /2x+1 f(x) =|

A: topic - functions

Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: Suppose f and g are positive functions. Is the following true or false? Vf,g:N → R f(x) E O(g(x)) =…

A: Big-Θ notation: A function g(n) is in Θ(f(n)) if there exist constants c1, c2, and N such that…

Q: Let f(x) = ln x and g(x) Show that f(x) and g(x) are both increasing when x > 0. Vr.

A: Given, f(x) = lnx When f(x) is increasing then f'(x) &gt; 0  Differentiating f(x) with respect to x…

Q: Find the first derivative of g(x) = 9eª sin(x²). g'(x) =

A: The given function .The aim is to find the derivative of the function.Note: Since you have posted…

Q: Suppose f: R → R is a function such that for all x, y ≤ R, f(x + y) = f(x) + f(y) and f(xy) =…

A:

Q: Suppose that f'(t)-29 (b)31 (e)none of these

A: Given: Suppose that f'(t)&lt;3 for all t in R and f(3)=1. To find: f(-7)  Lagrange’s mean value…

Q: a. Suppose that ƒ(x) = g(x³) + eg(3x) where g' and g" exist. Find f' and f" in terms of g' and g".…

A: Here we have given a composition of a function as given below.

Q: Suppose that F(x)=f(g(x)) and g(14)=2, g'(14)=5, f(14)-15, and f(2)=11. Find F(14). O 17 O 20 24 O…

A: Given query is to find indicated derivative

Q: Determine the main base function as one of f(x) = x, f(x) =x², f(x) = Vx , or f(x) = -. 1 а) h(x) —…

A: A)h(x)=x-7The function h(x) is obtained byvertical transformations of 7 units downof f(x)=xThe base…

Q: Let f(x) = 4 – a?, a > 0 f- (x) =

A: Given:- f(x) =4-x2  To find:- f-1(x)

Q: Use the quotient rule to show the following: If n is a negative integer, and g(x) = x" then g' (x) =…

A: Solving by Quotient rule we can get

Q: Let X~ N(1,4). What is E(X²)?

A: Here, it is given that X~N(1,4) that is X follows Normal distribution with mean μ=1 and variance…