1.) A random variable x has a density function given by: Sk(x + 1),0 < x < 2 0, elsewhere f(x) = c.) F (x) d.) Use F(x) to evaluate P(x > 2) and P(1 < x < 2.5) e.) Find u and o?
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Q: 1.) A random variable x has a density function given by: Sk(x + 1),0 1.5) c.) F (x)
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A: 7.52From the given information, the joint density function for X and Y is,
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Q: Find c. b. Find the cdf. c. What is P(.1≤ X <.5)
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A: a) The probability is P(X+Y≤12) = ∫01∫01/2 -x 24 xy dy dx=24∫01xy2201/2 -x dx=12x28+x44-x3301=12
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- Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise c=1/2 P(X < 1), Determine whether X and Y are independentIf X and Y are independent exponential random variables, each having parameter λ.(a) Find the joint density function of U = X + Y by using the convolution of fX and fY .(b) Find the joint density function of V = X − Y by using the method of transformation.(c) Are U and V independent?Suppose that the random variables X and Y have a joint density function given by: f(x,y)={cxy for 0≤x≤2 and 0≤y≤x, 0 otherwise Find the constant c, P(Y≥1/2), P(X < 2, Y >1/2), P(X < 1), Determine whether X and Y are independent.
- 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.Suppose that X has the density function c(x) = CX2 for 0 ≤ x ≤ 1 and f(x) = 0 otherwise.a. Find c.b. Find the cdf.c. What is P(.1≤ X <.5)?Let X be a continuous random variable with density function f(x) = 2x, 0 ≤ x ≤ 1. Find the moment-generating function of X, M(t), and verify that E(X) = M′(0) and that E(X2) = M′′(0).