Which of the following mathematical functions could be the CDF of some random variable?
Answer to relevant QuestionsSuppose a random variable is equally likely to fall anywhere in the interval [a, b]. Then the PDF is of the form Find and sketch the corresponding CDF. Repeat Exercise 3.1. A certain random variable has a probability density function of the form f x (x) = ce –2xu(x). Find the following: (a) The constant c, (b) Pr (X >2), (c) Pr (X < 3), (d) Pr (X < 3|X > 2). A Gaussian random variable has a probability density function of the form (a) Find the value of the constant. (b) Find the values of the parameters m and σ for this Gaussian random variable. Let W be a Laplace random variable with a PDF given by f w(w) = ce –2|w|. (a) Find the value of the constant c. (b) Find Pr (–1 < W < 2). (c) Find Pr (W > 0|–1 < W Suppose our receiver must observe the random variable and then make a decision as to what message was sent. Furthermore, suppose the receiver makes a three- level decision as follows: Decide 0 was sent if Pr (M = 0|X = x) ...
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