The R.V. X has the CDF F(x) = 1 - exp(-0.5 x) for 0<= x , a) Find the CDF of the random variate Y = X^3. b) Find the pdf of Y. c) Find the probability Y > 1
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The R.V. X has the CDF F(x) = 1 - exp(-0.5 x) for 0<= x ,
a) Find the CDF of the random variate Y = X^3.
b) Find the
c) Find the probability Y > 1
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- Consider two independent random variables X1 andX2 having the same Cauchy distributionf(x) = 1π(1 + x2)for − q < x < qFind the probability density of Y1 = X1 + X2 by usingTheorem 1 to determine the joint probability density ofX1 and Y1 and then integrating out x1. Also, identify thedistribution of Y1.Let Y1, Y2, ... , Yn be a random sample of size n from a gamma distribution with parameters α = 1and β = 2. Derive the probability distribution of the sample mean Y̅ using moment-generatingfunctions.What should be the value of a to make this continuous random variable X valid?
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