Take the Gamblers ruin on [0, N] with a fair coin, i.e., a simple random walk with absorbing boundaries at 0 and N. Let T be the time which elapses before the SRW is absorbed by one of the boundaries (i.e., the duration of the game. Show that P(T < ∞) = 1 and Epecation (T^k) < ∞ for all k.

Q: 15) A national distributor of pet toys determines the cost and revenue functions for one of its…

A: The cost function is given by C = 1.2x-0.0001x2 Revenue function is given by R = 3.6x-0.0005x2 To…

Q: Suppose X~N(196,20). Find x such that Pr(X > x) = 0.619.

A: The Z-score of a random variable X is defined as follows: Z = (X – µ)/σ. Here, µ and σ are the mean…

Q: Suppose that a new company begins its operations in 2020 and the size of the company over the next…

A:

Q: Consider a manufacturing firm that occupies one hectare of land. The firm trans- ports over half of…

A: According to the given information, it is required to draw the firm’s bid rent curve for x=0 to…

Q: Suppose that Saul has money in a savings account that pays him interest of 5% per year on the…

A:

Q: 3. Consider this function: g(x) =(r - 273) + 32. (a) Determine the function which will 'undo'…

A:

Q: Let X­­1 ~ Binomial(n1, p), and let X2 ~ Binomial(n2, p), independent of X1.  Show using a discrete…

A: It is given that: X­­1 ~ Binomial(n1, p) X2 ~ Binomial(n2, p) Y = X1 + X2

Q: 3. Consider f(x)=r. For which range of values will the function converge or diverge?

A:

Q: "Time headway" in traffic flow is the elapsed time between the time that one car finishes passing a…

A: d)

Q: Exercise 4. A train does not always leave precisely at its scheduled departure time. Let T be the…

A: The chances to catch the train will be as follows-

Q: Experiment X is consist of drawing two balls from a basket containing 13 blue and 5 red balls.…

A: Solution: From the given information, a basket contains 13 blue and 5 red balls. Total number of…

Q: 2-6. Identify the direction of increase in z in each of the following cases: *(a) Maximize z = X₁ -…

A: To find the direction of increase in z we draw the line considering a constant and as this is to be…

Q: The graph of y = 8x - x² and the line y = 7 for 0 ≤ x ≤ 7 is shown. 18 16 14 12 10 8 6 4 2 0- -1…

A:

Q: ad owns a company. However, his business is not going well. He projects that his continuous income…

A: Your given answer is approximately correct but You did mistake in round off to 2 decimal places

Q: (b) Pr[X > 0.6n] < 0.85. Let X be the number of HEADS after n fair coin tosses. Show that

A:

Q: Let f(t) = 2t² for -4 < t <4 and extend periodically. Compute: f(1) = f(5) = f(-4.5) = f(-8)= f(12)…

A: Periodic function: A function is said to be periodic with period T if f(x+T)=f(x).

Q: 3. Let f(x)= x+ - 8x2. What are the critical number(s)? a. X = = 0, x=-4, and x = 4 b. x = -2 and x…

A: Given a function f(x), critical numbers of the function f(x) are the values of x for which f'(x)=0…

Q: Find the initial value of the relation y = 3(x+3)² + 7

A:

Q: Use fixed point iteration to find p3 to the fixed point of g(x) = 2 . Let Po = 1. 0.635497846 O 0.5…

A:

Q: Which of the following is the jump discontinuity of f(x): |x-1 x² + x - 2 = OA. X-1 O B. *=2 В. C.…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.