1. Consider the following function
F(x) = {2x / 25 0<x<5
{0
otherwise
a) Prove that f(x) is a valid probability function.
b) Develop an inverse-transformation for this function.
c) Assume a multiplicative congruential random number generator
with parameters:
a: 23, m: 100, and xo: 17. Generate two random variates from the
function for (x).
a. For the following probability density
function:
f(X)=
3/4 (2X-X^2 ) 0 ≤ X ≤ 2
=
0 otherwise
find
its expectation and variance.
b. The two regression lines are 2X - 3Y + 6 = 0 and 4Y – 5X- 8
=0 , compute mean of X and mean of Y. Find correlation coefficient
r , estimate y for x =3 and x for y = 3.
Let f(x) = 5x+3 and g(x) =2x-5. Find (f+g)(x),(f-g)(x),(fg)(x),
and (f/g) (x). Give the domain of each.
(f+g) (x) =
(f-g)(x) =
(fg)(x) =
(f/g)(x) =
The domain of f+g is_
The domain of f-g is_
The domain of fg is _
The domain of f/g is _
Please at the end provide showed work.
Consider the root of function f(x) = x 3 − 2x − 5.
The function can be rearranged in the form x = g(x) in the
following three ways: (a) x = g(x) = x3 − x − 5 (b) x =
g(x) = (x 3 − 5)/2 (c) x = g(x) = thirdroot(2x + 5) For each form,
apply fixed-point method with an initial guess x0 = 0.5 to
approximate the root. Use the error tolerance = 10-5 to...
f(x)=〖2x〗^3-cosx/5+2e^(-x) given of f(x) function,
a-Fill the table f(x) column using calculator f(x) for
given x values.
b-After all calculation of table find f(1,3) Neville’s
Method approximation x0=1,2 and x1=1,4
c-Find f(1,3) Neville’s Method approximation x0=1,2
x1=1,4 and x3=1,5
Tell which result is more reliable and precise in case b, and c.
Why?
Suppose f is a twice differentiable function such that
f′(x)>0 and f′′(x)<0 everywhere, and consider the following
data table.
x
0
1 2
f(x) 3
A B
For each part below, determine whether the given values of A and
B are possible (i.e., consistent with the information about f′and
f′′ given above) or impossible, and explain your answer.
a)A= 5, B= 6
(b)A= 5, B= 8
(c)A= 6, B= 6
(d)A= 6, B= 6.1
(e)A= 6, B= 9
Suppose the function u(x) = 2x represents your taste over
gambles using an expected utility function. Consider a gamble that
will result in a lifetime consumption of x0 with probability p, and
x1 with probability 1 – p, where x1 > x0.
(a) Are you risk averse? Explain.
(b) Write down the expected utility function.
(c) Derive your certainty equivalent of the gamble. Interpret
its meaning.
(d) What is the expected value of the gamble?
(e) What is the risk...