Consider the following two fun9ctions:
y1= (x2+3x-1)/(x+4) ; y2= x-1+(3/x+4)
Perform long division on Y1 to verify it equals Y2
Consider the following two fun9ctions: y1= (x2+3x-1)/(x+4) ; y2= x-1+(3/x+4) Perform long division on Y1 to...
please answer questions 1-4
Divide using long division. (Show all work!) x2-x+3 6x2 +7x+5 3x-1 X+1 z! 15y3+y2–217 5y-3 2x3-29x+ x+4
Consider two random variables with joint density fY1,Y2(y1,y2)
=(2(1−y2) 0 ≤ y1 ≤ c,0 ≤ y2 ≤ c 0 otherwise
(a) Find a value for c. (4 marks) (b) Derive the density function
of Z = Y1Y2. (10 marks)
. Consider two random variables with joint density fyiy(91, y2) = 2(1 - y2) 0<n<C,0<42 <c o otherwise (a) Find a value for c. (4 marks) (b) Derive the density function of Z=Y Y. (10 marks)
x1 = 1, y1 = 2 x2 = 2, y2 = 3 x3 = 3, y3 = 0 x4 = 4, y4 = 4 x5 = 5, y5 = 7 Conduct a hypothesis test of whether there is a linear relationship between variable X and Y. Calculate the p-value of your test of significance.
(2) Given two independent variables X1 and X2 having Bernoulli distribution with parameter p=1/3, let Y1 = 2X1 and Y2 = 2X2. Then A E[Y1 · Y2] = 2/9 BE[Y1 · Y2] = 4/9 C P[Y1 · Y2 = 0) = 1/9 D P[Y1 · Y2 = 0) = 2/9 (3) Let X and Y be two independent random variables having gaussian (normal) distribution with mean 0 and variance equal 2. Then: A P[X +Y > 2] > 0.5 B...
Consider a random sample (X1, Y1),(X2, Y2), . . . ,(Xn, Yn) where Y | X = x is modeled by a N(β0 + βx, σ2 ) distribution, where β0, β1 and σ 2 are unknown. (a) Prove that the mle of β1 is an unbiased estimator of β1. (b) Prove that the mle of β0 is an unbiased estimator of β0.
483 – 5x² + 3x - 7 26. Given the rational function f(x) perform long division to find 2x2 - 3x + 1 the quotient, the remainder, and the slant asymptote. Show all work. bobsen espa Aldos os ovos gol Listen to monitoo lo on lle vode 275 25 Remainder: Quotient: Slant Asymptote: 11
Let Y1 and Y2 be two independent discrete random variables such that: p1(y1) = 1/3; y1 = -2 ,- 1, 0 p2(y2) = 1/2; y2 = 1, 6 Let K = Y1 + Y2 a) FInd the moment Generating function of Y1, Y2, and K b) find the probability mass function of K
Perform the indicated operations; simplify if possible: (x 4)x2 3x 2)
Let X1, X2, X3 be independent Binomial(3,p) random variables. Define Y1 = X1 + X3 and Y2 = X2 + X3. Define Z1 = 1 if Y1 = 0; and 0 otherwise. Define Z2 = 1 if Y2 = 0; and 0 otherwise. As Z1 and Z3 both contain X3, are Z1 and Z3 independent? What is the marginal PMF of Z1 and Z2 and joint PMF of (Z1, Z2) and what is the correlation coefficient between Z1 and Z2?
Perform the polynomial division using long division or synthetic division x 20. + 3x4 - x - 3 x + 3