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: The constant k which satisfies P(k <T < to.2) = 0.3 is: %3D А. -to.2 В. to.1 С. -to.1 D. None of the…

A: t distribution: Let us assume X is a random variable following standard normal distribution and Y is…

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: Q1: (): Let Y,., Y4 be order statistics of a random sample of size 4 from Exponential (10). Find…

A:

Q: (8) Let X-b(n, p), with E(X) = 6 and var(X) = 4.2, then P(X ≤ 6) = 0.608.

A: here given , E(X) = 6 var(X) = 4.2 for Binomial Distribution  mean = E(X) = np and Variance  = npq

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: Adam's value function is V(x) =, for gains (X 2 0) and (x) = - 3/Tx| for losses (X<0). Adam is…

A: Winning Utility Function V(x) = x4 Losing Utility Function V(x) = -3|x| Expected utility from the…

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: A bank teller series customers standing in the queue one by one. Suppose that the service time X,…

A: Answer: Using the given data,

Q: 1. Suppose the proportion P of correct encoding after t trials in a learning theory project is…

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: Suppose that r+ yl + lr - yl = 2. What is the maximum possible value of 2- 6z + y? (A) 5 (B) 6 (C) 7…

A: Consider a equation: x+y+x-y=2……1   and the expression, x2-6x+y2……2

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: G(n) = (d)o(d) is multiplicative function. If p is prime then G(p*), fork >1 equals dịn Select one:…

A:

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:

Q: (iv) p(39), where p is the Euler p-function.

A: Euler totient function and residue classes

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.