CALCULATE C(X1, X2) 4. Let X,,X, be two r.v.'s with m.g.f. given by M(t,,ty)=[} (+2 +1)...
4. Let X1, X, be two r.v.'s with m.g.f. given by M(t1, tz)=[] (en+2 +1)+] (e? +e?)]”, t1, tz € R. Calculate E(X1), oʻ(X,) and C(X1, X2), provided they are finite.
4. Let X1, X, be two r.v.'s with m.g.f. given by t +t 9 12 ' Calculate E(K), σ(K) and C(X1 , X2), provided they are finite.
Let X1 and X2 be two discrete random variables, where X1 can
attain values 1, 2, and 3, and X2 can attain values 2, 3 and 4. The
joint probability mass function of these two random variables are
given in the table below: X2 X1 2 3 4 1 0.05 0.04 0.06 2 0.1 0.15
0.2 3 0.2 0.1 0.1 a. Find the marginal probability mass functions
fX1 (s) and fX2 (t). b. What is the expected values of X1...
Let X be a r.v. with probability density function f(x)-e(4-x2), -2 < otherwise (a) What is the value of c? (b) What is the cumulative distribution function of X? (c) What is EX) and VarX
8. Let X1, X2,...,X, U(0,1) random variables and let M = max(X1, X2,...,xn). - Show that M. 1, that is, M, converges in probability to 1 as n o . - Show that n(1 - M.) Exp(1), that is, n(1 - M.) converges in distribution to an exponential r.v. with mean 1 as n .
O. Let X1 and X2 be two random variables, and let Y = (X1 +
X2)2. Suppose that E[Y ] = 25 and that the variance of X1 and X2
are 9 and 16, respectively.
O. Let Xi and X2 be two random variables, and let Y = (X1 X2)2. Suppose that and that the variance of X1 and X2 are 9 and 16, respectively E[Y] = 25 (63) Suppose that both X\ and X2 have mean zero. Then the...
"k)-T, E(X"k+1)-0, k = 0.1, m.g.f. of X and also its ch.f. Then deduce the distribution of X. 6. Let X be a r.v. such that E(X Find the
Let X1 and X be independent NO Fandom varables and let y=X1 + X2, Z= x² + x₂² a) Show that the joint MFG 0 (Y,Z) is My, z My,z (t1, tz) = (1-2+2) het - 272 if to ER and tz 2 / 2 by using a7 find Coot (Y, Z)
Let X1 and X2 be independent random variables so X1~ N(u,1) and X2 N(u,4) Where u R a) Show that the likelihood for , given that X1 = x1 and X2 = xz is 8 4T b) Show, that the maxium likelihood estimate for u is 4x1+ x2 и (х, х2) e) Show that СтN -("x"x) .я d) and enter a formula for the 95% confidence interval for
Let X1 and X2 be independent random variables so X1~ N(u,1) and...
1. Let X1 ~N(1,2) and X2 ~N(-1,2) be two Gaussian variables, and let Z = X1 +X2. (a) Express FX1 and FX2 in terms of Ф. b) Find Fz given that Xi, X2 are independent. (c)Find Fz given that it is Gaussian, and that E(X2-3
1. Let X1 ~N(1,2) and X2 ~N(-1,2) be two Gaussian variables, and let Z = X1 +X2. (a) Express FX1 and FX2 in terms of Ф. b) Find Fz given that Xi, X2 are independent....