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1. [7% of Exam] Decide which of the following statements are true and which are false. You do not need to justify your answers for the True/False questions! (a) (True or False) ________ If X is a continuous random variable on a probability space (?, ?, ?) and A is the event a < X ? b, then the conditional distribution function is given by F_{X|A}(x) = (F_X(x) - F_X(a)) / (F_X(b) - F_X(a)) (b) (True or False) ________ We say two continuous random variables X and Y are independent if we can write f_{XY}(x, y) = f_X(x)f_Y(y) for all x, y ? ?. (c) (True or False) ________ Suppose X and Y are jointly discrete random variables with joint mass function p_{XY}(x, y). If X and Y are dependent, then we can not determine the marginal probability mass functions p_X(x) and p_Y(y). (d) (True or False) If X ? N(?, ?²) = N(2, 9), then (X - 2) / 9 ? N(0, 1). If follows that ?(0 < X ? 3) = ?(1/9) - ?(-2/9). (e) (True or False) If X ? binom(n, p) where n is very large. Then we can approximate the binomial probabilities with a normal distribution. (f) (True or False) We say that a random variable X is a continuous random variable if its density function f_X is continuous. (g) (True or False) ________ We say that a random variable X is a discrete random variable if its image Im(X) is a countable set.

          1. [7% of Exam] Decide which of the following statements are true and which are false. You do not need to justify your answers for the True/False questions!

(a) (True or False) ________ If X is a continuous random variable on a probability space (?, ?, ?) and A is the event a < X ? b, then the conditional distribution function is given by F_{X|A}(x) = (F_X(x) - F_X(a)) / (F_X(b) - F_X(a))

(b) (True or False) ________ We say two continuous random variables X and Y are independent if we can write f_{XY}(x, y) = f_X(x)f_Y(y) for all x, y ? ?.

(c) (True or False) ________ Suppose X and Y are jointly discrete random variables with joint mass function p_{XY}(x, y). If X and Y are dependent, then we can not determine the marginal probability mass functions p_X(x) and p_Y(y).

(d) (True or False) ________ If X ? N(?, ?²) = N(2, 9), then (X - 2) / 9 ? N(0, 1). If follows that ?(0 < X ? 3) = ?(1/9) - ?(-2/9).

(e) (True or False) ________ If X ? binom(n, p) where n is very large. Then we can approximate the binomial probabilities with a normal distribution.

(f) (True or False) ________ We say that a random variable X is a continuous random variable if its density function f_X is continuous.

(g) (True or False) ________ We say that a random variable X is a discrete random variable if its image Im(X) is a countable set.

1. [7% of Exam] Decide which of the following statements are true and which are false. You do not need to justify your answers for the True/False questions!

(a) (True or False) If X is a continuous random variable on a probability space (?, ?, ?) and A is the event a < X ? b, then the conditional distribution function is given by FX|A(x) = (FX(x) - FX(a)) / (FX(b) - FX(a))

(b) (True or False) We say two continuous random variables X and Y are independent if we can write fXY(x, y) = fX(x)fY(y) for all x, y ? ?.

(c) (True or False) Suppose X and Y are jointly discrete random variables with joint mass function pXY(x, y). If X and Y are dependent, then we can not determine the marginal probability mass functions pX(x) and pY(y).

(d) (True or False) If X ? N(?, ?²) = N(2, 9), then (X - 2) / 9 ? N(0, 1). If follows that ?(0 < X ? 3) = ?(1/9) - ?(-2/9).

(e) (True or False) If X ? binom(n, p) where n is very large. Then we can approximate the binomial probabilities with a normal distribution.

(f) (True or False) We say that a random variable X is a continuous random variable if its density function fX is continuous.

(g) (True or False) We say that a random variable X is a discrete random variable if its image Im(X) is a countable set.

Added by Eric Z.

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