Question

can anyone provide any insight to this probability problem?

Answer 1

You are paid to forecast the value of some Bernoulli random variable Y
with parameter p. Assume that you forecast x, then you receive 3/16 − (Y − x)2
once the value of Y is known. When making your prediction, you know the p.m.f. of Y but you do not know Y. (a) What should your prediction x be in order to maximize the average amount of money that you make? In other words, how should you choose x so that the mean of (Y − x)2 is minimized? (

Answer 2

thats (Y-x)^2 btw

Answer 3

so y either has a value of 0 or 1 i believe. and a value of 1 with probability of p. so to maxamize would you want (3/16)-(y^2-2xy-x^2) to be maxamized?

Answer 4

part (b) says the following if it helps to make part (a) clear:
(b) You only want to accept this job if the expected amount of money that you make will be positive. For what distributions of Y would you make money on the average assuming you choose x optimally?

Answer 5

ok so maybe i have an idea. because y can only be 0 or 1. to minimize (y-x)^2 we would want x to be .5 i believe?

Answer 6

since (y-x)^2 has a range of 0 and up .... its minimum is 0

y-x = 0 when y=x , but im not sure what a pmf is so im prolly reading it wrong