Please give me specific steps, thanks!

(10%) Suppose you have three stocks in your portfolio. Weight and beta for each stock is denoted as wi and i for i=1,2,3. Suppose the correlation of each stock with the market portfolio is much less than 1 . Now, you learned in class that the standard deviation of a portfolio is less than the weighted average of the standard deviation of each stock in your portfolio due to the diversification effect. Thus, you conjecture that the same thing would be true for the beta of the portfolio. You think that by adding more stocks in your portfolio, you may get portfolio's beta to be lower than the weighted average of betas of stocks in a portfolio. Do you agree or disagree? Provide an intuitive explanation for your result