When fX(x) = {1/3, if −2<x≤1,
0, otherwise,
we have fY(y) = {g(y),if a<y≤b,
0,otherwise.
Give a formula for g(y) and the values of a and b using standard notation. (In your answers, you may use the symbol 'e' to denote the base of the natural logarithm.)
g(y)=
a=
b=
To find the formula for g(y) and the values of a and b, we need to determine the conditions under which fY(y) takes the value g(y).
Given that fX(x) = {1/3, if -2 < x ≤ 1,
0, otherwise,
we can determine the values of a and b by finding the range of x-values where fX(x) is non-zero.
From the given expression, we see that fX(x) is only non-zero for -2 < x ≤ 1. Therefore, we know that a = -2 and b = 1.
Now, to find g(y), we need to determine the value of fY(y) within the range (a, b). Since we are not given any specific information about fY(y) within this range, we can assign any function to represent g(y), as long as it is non-zero within the range (a, b).
Let's use a linear function as an example. We'll choose g(y) = mx + c, where m and c are constants.
Since a = -2 and b = 1, we have -2 < y ≤ 1.
Let's assume m = 1 and c = 1 as an example. This means g(y) = y + 1. Note that this is just an example, and any other function within the range (a, b) can be chosen.
Therefore, the formula for g(y) is g(y) = y + 1, and the values of a and b are a = -2 and b = 1.