Let X, Y, and Z be jointly continuous random variables. Assume that all conditional PDFS and expectations are well defined. E. g., when conditioning on X r, assume that x is such that fx (x)> 0. For the following formula, state whether it is true for all choices of the function g or false? E[g(Y) | Y= x] = ∫g(y) fY| X(y|x) dy

True

Step-by-step explanation:

Given that X,Y and Z are jointly continuous random variables

For : E [g(Y) | Y= x] = ∫g(y) fY| X ( y|x ) dy

For all choices of g the function is true given that g(y) = a random variable

A random variable is a variable with an unknown value it can be said to assign values to an experimental outcome.

soo this can be solve by using the formula:

f = p( 1 + i)^ n

where f is the future profit

p is the initial profit

i is the percent increase

n is the number of years

a . f = 30000 ( 1.05)^n

b. f = 30000 ( 1.05)^15

f = $62,368