Here we have used
Now we know that
The solution is as follows
4. Let X1, X, be two r.v.'s with m.g.f. given by M(t1, tz)=[] (en+2 +1)+] (e?...
CALCULATE C(X1, X2) 4. Let X,,X, be two r.v.'s with m.g.f. given by M(t,,ty)=[} (+2 +1) ++ (e? +e?)]”, tų, tz € R.
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 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 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
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...
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 .
6-x-4, 0x<2 0 1 2cych Exri If for two R.V. s X&Y the joint pdf is given by, otherwise Find Frix (o (1), Frix (alt), Ely/x-1]. var [Ylx-i] = E[^\x-]- (E[1\x=1])!
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...
4.(120) Let X1,,,Xn be iid r(, 1) and g(u) given. Let 6n be the MLE of g(4) (1)(60) Find the asymptotic distribution of 6, (2)(60) Find the ARE of T Icc(X) w.r.t. on P(X1> c), c > 0 is i n i1 5.(80) Let X1, ,,Xn be iid with E(X1) = u and Var(X1) limiting distribution of nlog (1 +). o2. Find the where T n(X - 4)/s. - 1 - 4.(120) Let X1,,,Xn be iid r(, 1) and g(u)...
Table 3.1 Time, t (s) Position, x (m) tn/t1 Time Squared, t^2 (s^2) (tn)^2/(t1)^2 xn/x1 t1, 0.40 x1, 0.25 1.0 .16 1 1 t2, 0.80 x2, 0.36 2.0 .64 4 1.4 t3, 1.2 x3, 0.52 3.0 1.4 9 2.1 t4, 1.6 x4, 0.71 4.0 2.6 16 2.8 t5, 2.0 x5, 0.95 5.0 4.0 25 3.8 t6, 2.4 x6, 1.2 6.0 5.8 36 4.8 Linear fit equation for Position Vs. Time: 0.545x - 0.0530 Quadratic fit equation for Position Vs. Time:...