ercise 6.2.2: Determining whether a subset of a vector space forms a subspace. info About Determine whether each subset of a vector space forms a subspace. (a) The subset W of Pn that contains all polynomials of degree n or less that have all negative coefficients. (b) The subset W=R+ of R where addition is defined as x+y=xy and scalar multiplication is defined as c⋅x=xc (c) The subset W of Rn×n for which the trace - the sum of the diagonal entries of a matrix - is zero. (d) The subset W of C[a, b] such that limx→x0f(x)=M where a

1. why is a frequency distribution useful? it allows researchers to see the "shape" of the data. it tells researchers how often the mean occurs in a set of data. it can visually identify the mean. it ignores outliers. 2. the is defined by its mean and standard deviation alone. normal distribution frequency distribution median distribution marginal distribution 3. approximately % of the data in a given sample falls within three standard deviations of the mean if it is normally distributed. 95 68 34 99 4. a data set is said to be if the mean of the data is greater than the median of the data. normally distributed frequency distributed right-skewed left-skewed