9. Assume the pdf of a continuous r.v. X is a even function, and its cdf is F(x). Prove that for any real number a > 0, we have a) F(-a)= 1- F(a) = 0.5 - f p(x) dx; b) P(|X|

Q: (9 pts.) Determine if the following function is continuous at x=-2. If not find the type of the…

A:

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that…

Q: 12. Examine the validity of the mean value theorem for: a) f(x) = lx² + mx + n in [a,b]

A: Consider the function fx=lx2+mx+n in a,b Here, the objective is to examine the validity of the mean…

Q: Let f(x) be a continuous function. If f(c) is an absolute max or absolute min, then c is unique. O…

A: Given,  fx is a continuous function fc is absolute max or absolute min , then c is unique.  We have…

Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: 1 = x² +1 1. Use the ed definition to prove that the function f(x) = (a) continuous at x = 0. (b)…

A:

Q: let f be the function x²-C for x< 5 flx)=3x+5c for X Z 5

A:

Q: Cx² f(x) = = if x 1 { 6 C-X

A:

Q: Let 4 – x² if x > 1 f(r) if x < 1 Determine whether or not f (x) is continuous at r = 1.

A: If left hand limit and right hand limit same, then f(x) is continuous at x=1.

Q: determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.

A: Given To evaluate the points where the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q    is…

Q: 4

A:

Q: (x² + 8, if x4) Consider the function f(x) = Find the value of B such that f (x) is continuous at x…

A:

Q: Determine L[f]if 0, f(1) = {1- 1, 0 2. 1,

A: Given that, A function f(t), t ≥ 0, its Laplace transform F(s) = L{f(t)} is defined as

Q: Find and classify the extreme values of f(r)=6r 4r over the interval (-2 21

A:

Q: Apply the Mean Value Theorem to f on the indicated interval. Find all values f(b) – f(a) b- a f' (C)…

A:

Q: Let f(x) = x. Show directly that f ∊ R[0, 2]

A:

Q: Let f be defined as follows: x²-9 f(x) = x-3 k if x # 3 if x = 3 What value of k would make the…

A:

Q: d. For each of the following, state whether the functions f: R → R, x → f(x) are injective,…

A: Given functions: fx=3x+2 fx=3x3-7x+3 fx=x6 fx=sinx fx=0.01x fx=4 We have to check whether the…

Q: B. Determine whether f(x) (x - 3) (2x + 1) (x + 4) is continuous at x= 3.

A:

Q: Suppose further that a <c< b. Which of the following is a property of an integral? O Option 1 Option…

A: