Applied Stochastic Processes Problem Set 2 Douglas Lanman
نویسنده
چکیده
At this point we recall the following procedure for generating a r.v. X with PDF FX(x) from a uniform r.v. Y . As stated on page 125 in [3], “...given a uniform r.v. Y , the transformation X = F−1 X (Y ) will generate a r.v. with PDF FX(x)”. Note that F −1 X (y) denotes the inverse function, such that F−1 X (FX(x)) = x [4]. From the plot of FX(x) shown in Figure 1(b), it is apparent that FX(x) maps x ∈ R onto the open interval (0, 1). As a result we only require a closed-form expression for the inverse PDF F−1 X (y) for y ∈ (0, 1). Application of the quadratic formula gives the following inverse functions.
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تاریخ انتشار 2007