Consider a continuous random variable X with the following PDF: L" 1

Consider a continuous random variable X with the following PDF: (a) (b) (c) (d) (e) (f) (h) (i) O othenvise Sketch the PDF of X. Be sure to label your a-xes. Determine the value of c that satisfies the normalization property. Set c to this value for the remainder of the problem. This can be done without integration, so your answer should be a number. What is the expected value of X? What is the variance of X? What is E[2X2 - + 1]? Calculate the probability that IXI is less than 2. (Your answer can be an integral, but you can also take advantage of the simple structure of the PDF.) Let B = 2). Determine the conditional PDF of X given the event {X B}. Calculate the probability that X < O given that IXI is less than 2. Calculate the conditional expectation E[XIBI of X given that IXI is less than 2.