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If a variable x takes values 0,1,2,3,…,n...

If a variable x takes values 0,1,2,3,…,n with frequencies proportional to binomial coefficients `n_(C_(0)), n_(C_(1)), n_(C_(2)),….,n_(C_(n))` then show that the mean of x is `(n)/(2)`

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If a variable takes the values 0, 1, 2,…,n with frequencies proporiotnal to binomial coefficient n_(C_(0)), n_(C_(1)), n_(C_(2)),….n_(C_(n)) , then mean of distribution is

The A.M. of the series .^(n)C_(0), .^(n)C_(1), .^(n)C_(2),….,.^(n)C_(n) is

C_0-(C_1)/(2)+(C_2)/(3)-…...+(-1)^n (C_n)/(n+1)=

2.(C_2)/(C_1)+3.(C_3)/(C_2)+…...+n. (C_n)/(C_(n-1))=

(C_1)/(C_0)+2. (C_2)/(C_1)+3. (C_3)/(C_2)+….+n.(C_n)/(C_(n-1))=