For two random variables X and Y that follow exponential distributions with rates λ1 and λ2 respectively, calculate E(E(X|Y )) when the correlation between X and Y is ρ = 0.5.
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For two random variables X and Y that follow exponential distributions with rates λ1 and λ2 respectively, calculate E(E(X|Y )) when the
Given that, two random variables X and Y that follow exponential distributions with rates λ1 and λ2 respectively, and the correlation between X and Y is ρ = 0.5.
We need to find E(E(X|Y )).
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- For 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).1. Consider the Gaussian distribution N (m, σ2).(a) Show that the pdf integrates to 1.(b) Show that the mean is m and the variance is σ.The time X of a radioactive isotope decays with an expected value of 10 years, and is modeled as an exponential random variable. a) What is the parameter λ of the exponential RV X? b) Compute P(X < 10).
- let X and Y are two random variables with p.d.f as f(x,y)=3x2y+3yx2 0<x<1 0<x<1.find conditional density of X given Y?.Find mean mode and standard deviation of r.v Y?. Correlation between X and Y?. check that X and Y are independent or not?.The random variables X and Y have the joint density: fX,Y(x,y) = 2−x−y, for 0<x<1, 0<y<1 0, otherwise For each of the following, please provide your answers in three decimal places: (a) What is the expected value of X? (b) What is the variance of X? (c) What is the covariance of X and Y? (d) What is the correlation of X and Y?If the probability mass function of the variable X described in the table is. find variance Y=x^2+4x If you know that the torque is of the second order of the variable X about the origin is equal to 2.85