A block cipher is an encryption algorithm that transforms a fixed-length block of unencrypted text data (called plaintext) into a block of encrypted text data (called ciphertext) of the same length for security purposes. A group of Korean communications engineers have designed a new linear approximation method for breaking a block cipher (IEICE Transactions on Fundamentals, Jan. 2005). The researchers showed that the success rate Y of the new algorithm has a beta distribution with parameters α = n/2 and β = N/2n , where n is the number of linear approximations used and N is the number of plaintexts in the encrypted data.
a. Give the probability density function for Y.
b. Find the mean and variance of Y.
c. Give an interval which is likely to contain the success rate, Y.