Answer the following questions in short: Show that if n numbers are drawn at random without replacement from the set (1, 2, 3, ..., N), then `var (barX) = ((N+1)(N-n))/(12n)`.

Answer the following questions in short: A box-contains ten tickets numbered 1 to. 10. Let X be the largest number drawn in n random draws with replacement. Obtain probabil ity mass function of X.

If the number of elements of set A are n, then show that the number of sub sets of A are 2^n .

Show that for a set of first n (le 2) natural number n < [n+1/2]^n

Statement 1: Out of 5 tickets consecutively numbered, three are drawn at random. The chance that the numbers on them are in A.P. is 2//15 . Statement 2: Out of 2n+1 tickets consecutively numbered, three are drawn at random, the chance that the numbers on them are in A.P. is 3n//(4n^2-1) .

The total number of binary operations on the set S={1,2} having 1 as the identity element is n . Find n .

Show that if n_(1) , n_(2) , n_(3) , n_(4) .... are the fundamental frequencies of the segments into which a string is divided by placing a number of bridges below it . The frequency of the string is given by (1)/(n) = (1) /(n_(1)) + (1)/(n_(2)) + (1)/(n_(3))+ ...

The total number of ways of selecting two numbers from the set {1,2, 3, 4, ........3n} so that their sum is divisible by 3 is equal to a. (2n^2-n)/2 b. (3n^2-n)/2 c. 2n^2-n d. 3n^2-n

If the mean of the set of numbers x_1,x_2, x_3, ..., x_n is barx, then the mean of the numbers x_i+2i, 1 lt= i lt= n is

Fill in the blanks If the mean of n numbers x_1,x_2,x_3,….,x_n is barx then the mean of kx_1,kx_2,kx_3,…,kx_n is______.

If ZZ is the set of intergers and n in ZZ, then the value of n(n+1) (2n +1) -