Question

Problem 1 True or False (5 pts) Circle the correct answer (0.5 pts each). (a) (True/False) For any two matrices A and B, AB = BA (b) (True/False) If X is a discrete random variable, then for any constant c, P(X = c) ? 0. (c) (True/False) If two events are disjoint or mutually exclusive and both have nonzero probability, then they cannot be independent. (d) (True/False) K = \begin{Bmatrix} \begin{bmatrix} a_1\\a_2\\a_3 \end{bmatrix}, \begin{bmatrix} a_4\\a_5\\a_6 \end{bmatrix} \end{Bmatrix} is possibly a basis of R$^3$ (e) (True/False) If X is a normally distributed random variable, any linear transformation of X will also be normally distributed. (f) (True/False) If events A$_1$, A$_2$,..., A$_n$ are pairwise independent, then they cannot be mutually independent. (g) (True/False) We have an urn with r red balls and b blue balls. We draw n balls from the urn without replacement. Let X = the number of red balls drawn. V(X) = nrb/(r+b)$^2$. (h) (True/False) The cdf F(x) of any random variable X is always a monotonic function of x. (i) (True/False) If X ~ Bin(n,p), then 1-X ~ NBin(n, 1-p). (j) (True/False) 2 linearly independent vectors can produce a non-zero dot product.

          Problem 1 True or False (5 pts)
Circle the correct answer (0.5 pts each).
(a) (True/False) For any two matrices A and B, AB = BA
(b) (True/False) If X is a discrete random variable, then for any constant c, P(X = c) ? 0.
(c) (True/False) If two events are disjoint or mutually exclusive and both have nonzero probability,
then they cannot be independent.
(d) (True/False) K = \begin{Bmatrix} \begin{bmatrix} a_1\\a_2\\a_3 \end{bmatrix}, \begin{bmatrix} a_4\\a_5\\a_6 \end{bmatrix} \end{Bmatrix} is possibly a basis of R$^3$
(e) (True/False) If X is a normally distributed random variable, any linear transformation of X will
also be normally distributed.
(f) (True/False) If events A$_1$, A$_2$,..., A$_n$ are pairwise independent, then they cannot be mutually
independent.
(g) (True/False) We have an urn with r red balls and b blue balls. We draw n balls from the urn
without replacement. Let X = the number of red balls drawn. V(X) = nrb/(r+b)$^2$.
(h) (True/False) The cdf F(x) of any random variable X is always a monotonic function of x.
(i) (True/False) If X ~ Bin(n,p), then 1-X ~ NBin(n, 1-p).
(j) (True/False) 2 linearly independent vectors can produce a non-zero dot product.

Problem 1 True or False (5 pts)
Circle the correct answer (0.5 pts each).
(a) (True/False) For any two matrices A and B, AB = BA
(b) (True/False) If X is a discrete random variable, then for any constant c, P(X = c) ? 0.
(c) (True/False) If two events are disjoint or mutually exclusive and both have nonzero probability,
then they cannot be independent.
(d) (True/False) K =
< b m a t r i x >
,
< b m a t r i x >
is possibly a basis of R^3
(e) (True/False) If X is a normally distributed random variable, any linear transformation of X will
also be normally distributed.
(f) (True/False) If events A1, A2,..., An are pairwise independent, then they cannot be mutually
independent.
(g) (True/False) We have an urn with r red balls and b blue balls. We draw n balls from the urn
without replacement. Let X = the number of red balls drawn. V(X) = nrb/(r+b)^2.
(h) (True/False) The cdf F(x) of any random variable X is always a monotonic function of x.
(i) (True/False) If X Bin(n,p), then 1-X NBin(n, 1-p).
(j) (True/False) 2 linearly independent vectors can produce a non-zero dot product.

Added by Valerie M.

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