Question

Given The Logistic Function: Σ(X)=1+E−X1 Define Σ′(X) In Terms Of Σ(X) [Show All The Steps]. What Can You Conclude? Question 2: You Are Given The Following Training Set {X(I)∈R,Y(I)∈[0,1]},I=1,2,…,M. You Notice That 90% Of Your Data Has Y(I)=0 And Only 10% Represent Y(I)=1. What Would You Do To Build Your Classifier Model? Case 1: You Have Only A

Answer 1

To find Σ'(X), take the derivative of Σ(X) using the chain rule. The derivative of Σ(X) is -E^(-X/1).

Step-by-step explanation:

To find Σ'(X), we need to take the derivative of Σ(X) with respect to X. The derivative of a function is a measure of how the function changes as its input changes. In this case, we have Σ(X) = 1 + E^(-X/1).

Taking the derivative of Σ(X) with respect to X, we can use the chain rule. Let's start by finding the derivative of the exponential function E^(-X/1). The derivative of E^(-X/1) is -1 * E^(-X/1).

Now, let's differentiate the entire function Σ(X) = 1 + E^(-X/1). The derivative of 1 is 0, and the derivative of E^(-X/1) is -1 * E^(-X/1). Therefore, Σ'(X) = 0 - 1 * E^(-X/1), which simplifies to Σ'(X) = -E^(-X/1).

From this result, we can conclude that the derivative of Σ(X) is -E^(-X/1).