Solve the initial value problems in Exercises

Probability and Statistical Inference 9
(Michigan Mathematics Prize Competition, 1992, Part II) From the set \(\{1,2,3, \ldots, n\}\), \(k\) distinct integers are selected at random and arranged in numerical order (from lowest to highest). Let \(P(i, r, k, n)\) denote the probability that integer \(i\) is in position \(r\). For example, ob

Mathematical Statistics with Applications 7
Let \(p(y)\) denote the probability function associated with a Poisson random variable with mean \(\lambda\) a. Show that the ratio of successive probabilities satisfies \(\frac{p(y)}{p(y-1)}=\frac{\lambda}{y}\), for \(y=1\), 2,.... b. For which values of is \(p(y)>p(y-1)\)? c. Notice that the resul

Chemistry 11
An iron bar weighed 664 g. After the bar had been standing in moist air for a month, exactly one-eighth of the iron turned to rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\). Calculate the final mass of the iron bar and rust.

Myers' Psychology for AP 2
Why is an operational definition necessary when reporting research findings? a. An operational definition allows others to replicate the procedure. b. An operational definition provides more context and includes many examples of the concept described. c. An operational definition is easier to transla

Organic Chemistry 9
Do the following electrocyclic reactions take place in a conrotatory or disrotatory manner? Under what conditions, thermal or photochemical, would you carry out each reaction? (a) H H (b) H H

Human Anatomy & Physiology 9
The velocity of nerve impulse conduction is greatest in (a) heavily myelinated, large-diameter fibers, (b) myelinated, small-diameter fibers, (c) nonmyelinated, small-diameter fibers, (d) nonmyelinated, large-diameter fibers.

Quantitative Chemical Analysis 8
Consider the titration of 25.00 mL of 0.082 30 M KI with 0.051 10 M AgNO3. Calculate pAg at the following volumes of added AgNO3: (a) 39.00 mL; (b) Ve; (c) 44.30 mL.

Biology: The Dynamic Science 5
While walking in the woods, you discover a large rock covered with a gelatinous, sticky substance. What test could you perform to determine whether the substance is inanimate, alive, or the product of a living organism?