2. Suppose that f(x) = e * for 0< x. a. Determine x such that P(x < X) = 0.40 b. Determine x such that P(X s x) = 0.40

Q: Suppose that a continuous function g satisfies: | 9(2)de = 12 and | 9(20)da = 24. Find og(3x²)dx.

A: Given that, ∫03gxdx=12, ∫06g2xdx=24 Let  ∫06g2xdx=24 Apply the substitution u = 2x to find this…

Q: 25. Let f: R→ R and let f(x) > 0 for all x € R. Show that f(x) is strictly decreasing if and only if…

A: We use the very basic inequality to solve this problem. Note that if x&lt;y then 1/x &gt; 1/y. This…

Q: of the function f(r) = (" – x)*. Find ao a. 12 Ob. O C. 6.

A: Let us consider the limit to be (0,2π) For the limit (-π,π)  the function is odd function so it will…

Q: 3. Let f(x)=x2+kx and g(x)=x+k . The graphs of f and g intersect at two distinct points. Find the…

A: Simple graph intersecting problem....

Q: Which of the following functions are continuous on the interval 1 < x < 7? A. h(x) B. f(x) = 2² +²36…

A: In this question, we will check the given function is continuous.

Q: Let giả tác reo f(x)=7r+k 5 ≤x≤ 10 *+80 *>10

A:

Q: Part. f. True or False: g(x) = In(x-1) is continuous for x > 1. 4 x +22

A:

Q: Let X={X1, X2, X3, X4, X5) and A = 0.7

A: Given: To explain the correct option of the given statement as follows,

Q: Determine the absolute extrema of the function f(x) = (x-3)e* on the interval -2 ≤x≤1.

A:

Q: REVIEW: The range of basic sine and cosine functions -15 sin 0 s1 and 1s cos 0 S 1 - #3 For 0 sx <…

A:

Q: Find the value of the constant a that makes the following function continuous on (-∞, ∞). 5x³ + 5x²…

A: We need to find a value that makes the function continuous.

Q: Q4 Suppose X ~ Exp(A), calculate E[X|X > 1].

A: * SOLUTION :-  (4) As per given data the calculation is shown below

Q: 5. Consider the function g(x)=1 a) For what values of x is g(x) continuous? b) For what values of x…

A: In the question we have to find where function is continuous and differentiable.

Q: 2. Let g(x) = [x]. Find: 2.a g ¹({0}) 2.b g¹({-1,0,1}) 2.c g ¹({x 10 < x < 1}).

A:

Q: Determine the value A (to 2 decimal places) of the following p.d.f.: A(1-x²) -1<x<1 s(x)= otherwise…

A: Solution

Q: Suppose that f e H(C) and |f(2)I < eRez for all z. Show that f(z) ce for some constant c.

A: Consider fz=cez for z=x+i y Take absolute value on both sides: fz=cez=cex+iy=cexeiy=cex…

Q: Let f(x) = logox and g(x)=₁*. For all x g(x).

A:

Q: |4. Is f(x) = ()* increasing or decreasing?

A:

Q: 3 Let f (x) = iVx, 1 2) b. Find E[X] c. Find Var X

A: Solution: From the given information,

Q: 5. Find the value of k that makes the following function continuous. f(x) : ={2x - 1,if x2-1

A: