For a certain random variable X it is known that E[X]=2, Var(X)=3. What E[x']?
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![For a certain random variable X it is known that E[X]=2, Var(X)=3. What is
E[x*]?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbc553f1-6131-4f5e-b5e9-0aa3b55fe7e0%2F3d7741a9-e32d-4e77-a833-601c7ad4bf92%2Fedt4ntb_processed.png&w=3840&q=75)
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- Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln√X] using Jensen’s inequality.Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?X is an exponential random variable with λ =1 and Y is a uniform random variable defined on (0, 2). If X and Y are independent, find the PDF of Z = X-Y2
- Let X be a Gaussian random variable (0,1). Let M = ln(5*X) be a derived random variable. What is E[M]?If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?Consider a random variable X with E[X] = 10, and X being positive. Estimate E[ln square root(X)] using Jensen’s inequality.
- For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))If X is an exponential random variables with rate 1, then its distribution function is given by F(x) = 1 − e−x Show that x = − ln(1 − u).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).
- X is a continuous random variable taking values between 0 and 2. If F(1.5) = 0.70 and P(X<1) = 0.20, what is P (1 < X < 1.5)?For any continuous random variables X, Y , Z and any constants a, b, show the following from the definition of the covariance:X is an exponential random variable with parameter λ = 4 Calculate P {X ≤ 3