(a) Find P{X10 = 10}. (b) Approximate P{−10 ≤ X100 ≤ 10} using the central limit theorem. (c) Find P{Xn = k}. 2. Absolute-value random walk. Consider the symmetric random walk Xn in the previous problem. Define the absolute value random process Yn = |Xn|. (a) Find P{Yn = k}. (b) Find P{max1≤i<20 Yi = 10 |Y20 = 0}. 3. A random process. Let Xn = Zn−1 + Zn for n ≥ 1, where Z0, Z1, Z2, . . . are i....

4. Noise cancellation. A classical problem in statistical signal processing involves estimating a weak signal (e.g., the heart beat of a fetus) in the presence of a strong interference (the heart beat of its mother) by making two observations; one with the weak signal present and one without (by placing one microphone on the mother’s belly and another close to her heart). The observations can t...

To the Editor: It was disturbing to read the article entitled “Studies of the Stability of 18 Chemical Constituents,” in the December, 1972, issue of Clinical Chemistry (1). The authors define their conditions of collection and storage but do not, however, make it clear what their object is. If the objective was to show stability of serum before analysis, then their data are misleading. For exa...