Two random variables X and Y have the joint characteristic function • (0,0₂) = cxp{jn¸0,- / o; 0; + jn,‚0₂ - 12/0}{0}}} Find their means.
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- For a random variable X with mgf Mx(t)=exp{t^2−3t/2}; i) Find E[X] ii) Find E[X^2] iii) Find Var[X]let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x isPlease do not give solution in image format thanku 1.Suppose that the moment generating function of a random variable X is MX(t)=exp(2e^t−2) and that of a random variable Y is MY(t)=((4/5)e^t+1/5)^16. If X and Y are independent, find each of the following. (a) P{X+Y=2}= (b) P{XY=0}= (c) E[XY]= (d) E[(X+Y)^2]= ———
- Let random variables X and Y have the joint pdf fX,Y (x, y) = 4xy, 0 < x < 1, 0 < y < 1 0, otherwise Find the joint pdf of U = X^2 and V = XY.A random variable X has a pdf f(x) = { kex, x<0 0 , otherwise } Determine the value of k, and find V(x).3) Assume that a random variable X has moment generating function as follows: e' + e²¹ M(t)=4-2e¹ ∞ Calculate the mean and variance of X. for t9=17-41+2 =5 ab d be12-41+1=3 Evaluate the fo llowing intergral's nesn_x5 dn %3DFor an exponential random variable (X) having θ = 4 and pdf given by: f(x) = (1/θ)e^(−x/θ ) where x ≥ 0, compute the following: a) E(X). b) Var(X). c) P(X > 3).Please solve with the step max in 60-90 minutes the chapter actuarial Investigate whether the risk measure Variance principle premium p(L) = μL + ασL2 α = loading factor meets the axioms (T, S, PH and M)Suppose X is a random variable with the cdf Fy(x) = 1-(1+x²) x>0, c>0, Y>0 Derive the pdf of the inverse of X, Y=1/x²A variable X has a probability function f(x, 0) = 0e 0x; x≥0 y >0. The parameter 0 is estimated using two different estimators of simple random samples of size two: 01 2x+4x2 and 2=4x+5x2 3 3 Select the best estimator for \theta by comparing the Mean Squared Errors2) Let X be a continuous random variable with PDF 0SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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