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bos on 559 2. Random variable X and Y have a bivariate normal distribution. The conditional...
1. Use a normal-scores plot to see if the data are approximately normally distributed. 12, 14, 18, 22, 25, 29, 31 The data (does, does not) appear to be approximately normally distributed because the normal-scores plot (is, is not) roughly linear. 2. Random variable X and Y have a bivariate normal distribution. The conditional density of X given Y = y is a a. bivariate normal distribution b. chi-square distribution c. linear distribution d) normal distribution e. not necessarily any...
4. Use the distribution function technique to find the density function for Y = 2X + 3 The density function for X is f(x). Your answer should be given as a piecewise function. 2x + 1) 1<x<2 f(x) = 4 0 elsewhere =f2x+1) h 5. Use the transformation technique to find the density function for Y = 4x + 1. The density function for X is f(x). Your answer should be a piecewise function. f(x) = S4e-4x 0 < x...
The probability distribution for the random variable X is shown by the table. *Use the transformation technique* to construct the table for the probability distribution of Y = x^2 + 1. X = -2 -1 0 1 2 P(x) = 0.12 0.18 0.28 0.24 0.18
Suppose (X, Y ) has bivariate normal distribution, E(X) = E(Y ) = 0,V ar(X) = σX2 , V ar(Y ) = σY2 and Correl(X, Y ) = ρ. Calculate the conditional expectation E(X2|Y ). I. Suppose (X,Y) has bivariate normal distribution, E(X) = E(Y) 0, Var(X)-σ , Var(Y) σ and Correl (X,Y)-p. Calculate the conditional expectation ECKY expectation E(X2Y)
4. Let (X,Y) be a bivariate normal random vector with distribution N(u, 2) where -=[ 5 ], = [11] Here -1 <p<1. (a) What is P(X > Y)? (b) Is there a constant c such that X and X +cY are independent?
please help me 6. Suppose X, Y have a bivariate normal distribution with marginal dis- tribution X ~ N(0,1) and the conditional distribution of Y given X-x is N(ax + b,a?). (i). What is the marginal distribution of Y? (ii). What is the conditional dist ribut ion of X given Y-y?
If X and Y are two non-independent normal distribution whose joint distributions is bivariate normal with correlation p, what is Var(XY)?
The following table represents the probability distribution of a discrete variable x. What is the value of the unknown probability P (3) X P(x) 0 0.12 0.05 1 2. 0.24 3 P(3) 0.18
1. Consider a discrete bivariate random variable (X,Y) with the joint pmf given by the table: Y X 1 2 4 1 0 0.1 0.05 2 0.2 0.05 0 4 0.1 0 0.05 8 0.3 0.15 0 Table 0.1: p(, y) a) Find marginal distributions of X and Y, p(x) and pay respectively. b) Find the covariance and the correlation between X and Y.
Let X be a standard normal distribution. Let ξ be another random variable, independent of X, which can take only two possible values, say -1 and 1. Moreover, assume that Ele] = 0. ( . (b) Find COV(x,Y). (c) Are X and Y independent? (d) Is the pair (X,Y) bivariate normal? a) Find the distribution of Y -£X Let X be a standard normal distribution. Let ξ be another random variable, independent of X, which can take only two possible...