1. Let Fx, y) = 2xî – vì and let C-C, +C,, where is the horizontal...
Let $(x) = 2x2 and let Y = $(X). assume that Y ~ U(0,1/2) and that X is a continuous random variable. fx(x) = 0 whenever |2| > 1. Obtain an expression linking fx(x) to fx(-x) for xe (-1,1). Show that E[X] = -2/3 + 28. xfx(x) dx. Using your expression linking fx(x) and fx(-x), obtain an upper bound for E[X] and a pdf fx for which this bound is attained. [10]
Let fx) (5x2 2x + 20)/(3 - 7x2). The horizontal asymptote is given by y ? Round your answer to 2 decimal places. Your Answer: Answer
Let fx) (5x2 2x + 20)/(3 - 7x2). The horizontal asymptote is given by y ? Round your answer to 2 decimal places. Your Answer: Answer
Find the horizontal asymptote of the given function. 35) f(x) - 4x2.3 4x2.3 A) Y-3 C) y - 1 B) y--3 D) None Sketch the graph of the rational function. Indicate the equations of the vertical and horizontal asymptotes and the y-intercept. 40) f(x)* Vertical Asymptote: Horizontal Asymptote y-intercept 36) gix) x2 + 8x - 5 x-5 A) y - 5 C) None B) y = 0 D) y - 8 37)(x) x2.5 A) y = 0 C) None B)...
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter = 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(x > 0.25) U (Y > 0.25)}? (c) What is the conditional distribution of X. given that Y - 3? (d) What is Var(Y - E[2X] + 3)? (e) What is...
1. Let $(x) = 2x2 and let Y = $(x). (a) Consider the case X ~U(-1,1). Obtain fy and compute E[Y] (b) Now instead assume that Y ~ U(0,1/2) and that X is a continuous random variable. Explain carefully why it is possible to choose fx such that fx (2) = 0 whenever 21 > 1. Obtain an expression linking fx(2) to fx(-x) for 3 € (-1,1). Show that E[X] = -2/3 + 2 S xfx(x) dx. Using your expression...
1. Let Q1 = y(7), where y solves dy dx + 8x 2 = 5x, y(6) = 4. Let Q = ln(3 + |Q1|). Then T = 5 sin2 (100Q) satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — (E) 4 ≤ T ≤ 5. 2. Let Q1 = y(1), where y solves dy dx + 1.7y = 5e 1.2x...
Let U ~uniform(0,1). Let Y =−ln(1−U). hint: If FX (x) = FY (y) and supports x,y ∈ D, X and Y have the same distribution. Find FY (y) and fY (y). Now, it should be straight forward that Y follows distribution with parameter_____________-
12. Let X and Y be independent random variables, where X has a uniform distribution on the interval (0,1/2), and Y has an exponential distribution with parameter A= 1. (Remember to justify all of your answers.) (a) What is the joint distribution of X and Y? (b) What is P{(X > 0.25) U (Y> 0.25)}? nd (c) What is the conditional distribution of X, given that Y =3? ur worl mple with oumbers vour nal to complet the ovaluato all...
Let X and Y have joint probability mass function fX,Y (x, y) = (x + y)/30 for x = 0, 1, 2, 3 and y = 0,1,2. Find: (a) Pr{X ≤ 2, Y = 1}(b) Pr{X > 2, Y ≤ 1} (c) Pr{X +Y = 4}. (d) Pr{X > Y }. (e) the marginal probability mass function of Y , and (f) E[XY].
0 Sy s 1. Let X and Y have joint pdf: fx,y(x, y) = kx(1 – x)y for 0 < x < 1, (a) Find k. (b) Find the joint cdf of (X,Y). (c) Find the marginal pdf of X and of Y. (d) Find Pſy < 81/2],P[X<Y]. (e) Are X and Y independent? (f) Find the correlation and covariance of X and Y. (g) Determine whether X and Y are uncorrelated. (h) Find fy(y|x) (i) Find E[Y|X = x]...