Suppose we have an initially empty hash table Aſi…n] with n slots that resolves collisions through chaining. Moreover, suppose we insert n elements into this table such that each element inserted has a probability 1 to be put into slot A[i] independently of all other elements. Let Ri be the random variable that counts the number of elements that get hashed to slot A[i]. a. Give an expression in terms of n and k for Pr(Ri = k) (i.e., the probability that k elements get hashed to slot A[i]), where 0 <k <n. b. Prove that Pr(Ri = k) < Pr(R = k) = ()”, oskan , 0 <k <n Note, you may find the inequality (%) = (ne)* useful. Here e ~ 2.718 is Euler’s number, and you can assume the convention tha Show transcribed image text Suppose we have an initially empty hash table Aſi…n] with n slots that resolves collisions through chaining. Moreover, suppose we insert n elements into this table such that each element inserted has a probability 1 to be put into slot A[i] independently of all other elements. Let Ri be the random variable that counts the number of elements that get hashed to slot A[i]. a. Give an expression in terms of n and k for Pr(Ri = k) (i.e., the probability that k elements get hashed to slot A[i]), where 0

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