Suppose the market portfolio is equally likely to increase by $33\%$ or decrease by $8\%.$

a$.$ Calculate the beta of a firm that goes up on average by $26\%$ when the market goes up and goes down by $9\%$ when the market goes down.

b$.$ Calculate the beta of a firm that goes up on average by $25\%$ when the market goes down and goes down by $27\%$ when the market goes up$.$

c$.$ Calculate the beta of a firm that is expected to go up $4\%$ independently of the market.