Suppose that Y. Y...., Y's denotes a random sample from a uniform distribution defined on the...

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Suppose that Y₁. Y₂...., Y's denotes a random sample from a uniform distribution defined on the interval (0, 1). That is, 0sysl. ro) = {0: -lo, elsewhere. Find the density function for the second-order statistic. Also, give the joint density function for the second- and fourth-order statistics. Let Y₁ and Y₂ be independent and uniformly distributed over the interval (0, 1). Find a the probability density function of U₁ = min(Y₁. Y₂). bE (U₁) and V (U₁). Let Y₁. Y₂...., Y, be independent, uniformly distributed random variables on the interval [0,0]. Find the a probability distribution function of Y=max(Y₁. Y2..... Ya). b density function of Yon). c mean and variance of Y() Show that for random samples of size n from an exponential population with the parameter 0, the sampling distributions of Y, and Y, are given by for y₁0 elsewhere and 81 (31)= 8n(n)= 0 -e-Ya/11-e-Yn/-1 for yn>0 elsewhere Let Y₁. Y... Y, be independent random variables, each with a beta distribution, with a = ß = 2. Find a the probability distribution function of Y)= max(Y₁. Y2..... Ya). b the density function of Y(). c E(Y)) when n = 2. Find the probability that the range of a random sample of size 1 from the population fx(x)=2e-2 for x ≥0 does not exceed 4. Suppose that Y₁. Y₂...., Y's denotes a random sample from a uniform distribution defined on the interval (0, 1). That is, 0sysl. ro) = {0: -lo, elsewhere. Find the density function for the second-order statistic. Also, give the joint density function for the second- and fourth-order statistics. Let Y₁ and Y₂ be independent and uniformly distributed over the interval (0, 1). Find a the probability density function of U₁ = min(Y₁. Y₂). bE (U₁) and V (U₁). Let Y₁. Y₂...., Y, be independent, uniformly distributed random variables on the interval [0,0]. Find the a probability distribution function of Y=max(Y₁. Y2..... Ya). b density function of Yon). c mean and variance of Y() Show that for random samples of size n from an exponential population with the parameter 0, the sampling distributions of Y, and Y, are given by for y₁0 elsewhere and 81 (31)= 8n(n)= 0 -e-Ya/11-e-Yn/-1 for yn>0 elsewhere Let Y₁. Y... Y, be independent random variables, each with a beta distribution, with a = ß = 2. Find a the probability distribution function of Y)= max(Y₁. Y2..... Ya). b the density function of Y(). c E(Y)) when n = 2. Find the probability that the range of a random sample of size 1 from the population fx(x)=2e-2 for x ≥0 does not exceed 4.

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