Suppose· X · has probability-density-function (p.d.f) fx(x) = 7(1+x²)³ ° which one is the p.d.f.. for Y=2X. A 2 fr(y)= π(4+ y²) B f(y)=- 1 π(1+4y²) fx(y)= 1 л(1+y²) 1 fr(y) == arctan y π C D
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- 6.) Suppose X is continuously uniformly distributed on [−2, 2]. Let Y = X2. What is the density function of Y? What is the expected value of Y?1) Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the estimator of moments for the parameter θ.5.)Suppose X is continuously uniformly distributed on [1, 4]. Let Y = ln(X). What is the density function for Y ? (Include the bounds for Y .)
- 4. A continuous random variable x that can assume value between x = 2 and x = 5 has a density function given by f(x) = 2/27 (1 + x). Find a) P (x < 4) and b) P (3 < x < 4)1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.For random variables X and Y with joint density function f(x,y) = 6e^-2x-3y. (x,y > 0) and f(x,y) = 0 otherwise, find: Are X and Y independent? Give a reason for your answer.
- A continuous variable Y has a probability density function given by p(y)=Ay^3 for 0≤y≤3 What is the probability that we find Y=3?Let the joint Probability Density Function of X and Y be: 2*e(x+y) for -infinity<x<y<1. Find the Cov(X, Y) and find the Marginal Probability Density Functions of X and Y8. Show that the gamma density function f(x, λ, r) integrates to 1
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