Its macroeconomic question

Question One 1. Write down the definition of a cumulative distribution function (CDF). Explain what it means in words, perhaps using an example. 2. Verify whether the following function is a valid CDF. If yes, draw a graph of the corresponding PDF. F, (x) Image by MIT OpenCourseWare. 3. Verify that the following function is a valid PDF and draw the corresponding CDF. F. (x 1 Image by MIT OpenCourse Ware. Question Two 1. Give a p.d.f. whose c.d.f. is not continuous but is right-continuous. True/false/uncertain: Always give a brief explanation if the statement is true, or counter-examples and a short explanation of the counter-examples if the statement is false or uncertain. 1. If P(A|B) > P(A) and P(AJC) > P(A), then P(A|B, C) > P(A). 2. A continuous p.d.f. can never take a value greater than 1. 3. P(A) = P(A|B) P(B) means that A and B are independent. Question Three (Source: Bain/Engelhardt, Ch. 2, ex. 8) A nonnegative integer-valued random variable X has a CDF of the form F(x) = 1 - (1/2)3+1 for x = 0, 1, 2, .. . and zero if r 0 for & 5 0 1. Determine the PDF for Y = X!. 2. Determine the PDF for W = Xe for ke N. Question Two Suppose that the PDF of a random variable X is as follows: f(x) = BT for 0 ) for 0