a. What value of c will make f(x) a valid density? b. What is P(X = 1)? What about P(X = 1 or X = 2)? c. Find E(X).

Q: Exercise 2. Prove that dim(null T") = dim(null T) + dim W – dim V and dim(range T") = dim(range T),…

A: We prove dim null T*=dim null T + dim W-dim V and dim range T *=dim range T for every T L(V·W).

Q: Estimate U, and find the relative uncertainty in the estimate, assuming that X = 5.0 ± 0.2, Y = 12.0…

A: To find the U=XY as shown below, U=5.0×12.0U=7.7459

Q: 9. If f is continuous and | f(x) da = 3, find æf(x?) dx.

A: We have to evaluate the given definite integral using the other definite integral.

Q: Let g(u) be a function such that f g(u) du = ln (1 + 8u²) + C. Evaluate fxg(x²) dx.

A: This question can be solved using the concept of integration by substitution and definite integrals.

Q: Evaluate | re dx by changing from x-limits to u-limits. xet

A: Explanation of the solution is given below...

Q: Is the following statement true or false? Let f(x) = e- if a 21 and f(x) = 0 if x < 1. Then f(x) is…

A: Given function is f(x) = e-xifx≥10ifx&lt;1

Q: Let f (x) = for 1 < x < 5 be a pdf. Find c. Round to three decimal places as needed.

A: Assume that X is a continuous random variable with probability function f(x).

Q: The PDF of a continuous r.v. X is given byfX(x) = a + bx2 if 0 ≤ x ≤ 1            0 otherwise.What…

A: Given:The probability density function (PDF) fX(x):fX​(x)=a+bx2 if 0≤x≤1fX​(x)=0 otherwiseandE(X) =…

Q: For the following continuous joint PDF, nd: E(X). 8.123x5 (y²+3)8, for 0.2 < x < 0.3, and 0.4 < y <…

A:

Q: 1. If the joint PDF of X and Y is -1<x<y<1 otherwise c, fxx(x, y) = {6" {o,

A:

Q: Find the absolute extrema of the function on the closed interval. y = x ln(x + 4), [0, 3]

A: Given function: y=x lnx+4,0,3 First we shall diffrentiate the function to determine the critical…