Suppose that X, and X2 are aiscrete random variables with joint pdf of the form f(x1,x2) = c(x1 + x2), x1 = 0,1,2; x2 = 0,1,2 %3D
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- An ordinary (fair) coin is tossed 3 times. Outcomes are thus triple of “heads” (h) and tails (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of tails in each outcome. For example, if the outcome is hht, then R (hht)=1. Suppose that the random variable X is defined in terms of R as follows X=6R-2R^2-1. The values of X are given in the table below. A) Calculate the values of the probability distribution function of X, i.e. the function Px. First, fill in the first row with the values X. Then fill in the appropriate probability in the second row.The 4-dimensional random vector X has PDF fX(x)={1 when 0≤xi≤1, i=1,2,3,4 and 0 otherwise}. Are the for components of X independent random variables?Suppose X is random variable whose p.d.f. is f2)=(2x-x²), 0, OSxs2 Suppose X is random variable whose p.d.f. is f(x)={4 elsewhere Find the mode , if it exists.
- Suppose that the random variables X and Y are independent with Var(X)=8 and Var(Y)=6. Calculate Var(5X−7Y+17)Let P and Q be two independent Random variables with Var(P) = 5 and Var(Q) = 4. Find Var(7P+4Q-1).Let X and Y are 2 independent random variables N (0,1) Questions: how to find E(X), E(Y), E(X^2), E(Y^2)? Thank you
- Two cards are drawn at random from a box which has 5 cards numbered 1,2,3,4 and 5. Find the joint probability function of (X,Y) where X represents the sum and Y represents the maximum of the two numbers drawn. Also, find the correlation coefficient between X and Y.Show that two random variables X, and X, with joint pdf. Sx, x, (*1 »*2) = 16 Xl< 4, 2< X2<4 are independent and orthogonal.Suppose X, Y and Z are independent random variables with var (X) = 4 , var (Y) = 4 , var (Z) = 1/n Find: var (X/2 - Y + the square root of nZ) (divided by -2)
- Let X ~ N(0, 2) and Y ~ covariances Cov(X,Y) and Cov(Y, X +Y). Exp(A = 3) be two uncorrelated random variables. Find theQ2) A continuous random variable has PDF Kx²+2x+1, -25x5 3. Find K, P(x)>0. X, X² and ¹.Suppose X~ Binom(6, p) and define an estimator T ==to estimate p. Then, variance 6. of T is, p(1–p) a) Var (T)= 6. b) Var (T) = 6 p(1 – p) c) Var (T)~ p(1-p) d) Var (T) - 36р