O retorno mensal de certo investimento de risco pode ser modelado pela variável aleatória W, com função de probabilidade dada a seguir. mathrm(W) & -5 % & 0 % & 5 % & 10 % & 15 % mathrm(P)(mathrm(W)=mathrm(w)) & 0,4 & 0,15 & 0,25 & 0,15 & 0,05 O retorno esperado é: A -0,5 % . B 0,5 % . C 1,5 % . D 5 % . E 7,5 % .

## Step 1: Understand the Problem### We are given a probability distribution for the monthly return of a risky investment. The table provides possible returns and their associated probabilities. We need to calculate the expected return.## Step 2: Define the Expected Value Formula### The expected value \( E(W) \) of a discrete random variable is calculated using the formula: where are the possible values of , and \( P(W = w_i) \) are their respective probabilities.## Step 3: Apply the Values from the Table### Using the values from the table:- , \( P(W = -5\%) = 0.4 \)- , \( P(W = 0\%) = 0.15 \)- , \( P(W = 5\%) = 0.25 \)- , \( P(W = 10\%) = 0.15 \)- , \( P(W = 15\%) = 0.05 \)## Step 4: Calculate the Expected Return### Substitute these values into the expected value formula: ### Simplify each term:- - - - - ### Sum these results: