There are 4 unrelated parts to this question. Justify your answers
a) (i) if 8 identical blackboards are to be divided among 4 schools, how many divisions are possible?
(ii) if 8 new teachers are to be divided among 4 schools, how many divisions are possible?
b) show that for any nonnegative integer n we have (n0)+(n2)+(n4)+......=(n1)+(n3)+(n5)+.... { note- (no) means nC0)
(Hint: use the binomial theorem ans substitute in specific values for x and y to prove the above statement)
c) suppose X is a continous random variable with density fX(x) for all x belongs to R. find the density of Z= (X-?)/?, for some constants ? and ? not equal to zero