Please answer the Q2 and Q3. Maximum Likelihood Estimation1. Find the MLE of based on a random sample X₁, X₂, ..., X₁ from each of the followingp.d.f.'s.(a)where 0 < x < 1, 0 < 0, and 0 otherwise.(b)f(x0) = 0x0-1f(x|0) = (0+1)x-⁰-2where 1 < x, 0 <0, and 0 otherwise.(c)where 0 < x, 0 <0, and 0 otherwise.(d)f(c\0) = 02re-trxef(x0) = 0(1-0)-1for x = 1, 2, ..., 0 < 0 < 1, and 0 otherwise2. Find the asymptotic variance of the MLE in each part of question 1.Xn3. Consider two independent random samples X₁, X2, ..., X₁N(μ, σ2).~ N(µ, o²) and Y₁, Y2, ..., Ym~(a) Using the data from the two random samples find the m.l.e. of µ, o², and o².(b) Find the asymptotic variance of μ.

As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted...…

1. Find the MLE of based on a random sample X₁, X₂, ..., Xn from each of the following p.d.f.'s. (a) where 0 < x < 1, 0 < 0, and 0 otherwise. (b) f(x|0) = 0x0-1 f(x|0) = (0+1)x-0-2 where 1 < x, 0 <0, and 0 otherwise. (c) where 0 < x, 0 <0, and 0 otherwise. (d) f(z|0) = 02re-e f(x|0) = 0(1-0)²-1 for x = 1,2,..., 0 < 0 < 1, and 0 otherwise 2. Find the asymptotic variance of the MLE in each part of question 1. 3. Consider two independent random samples X₁, X2, ..., X₂ ~ N(μ, o?) and Y₁, Y2, ..., Ym N(μ, σ2). (a) Using the data from the two random samples find the m.l.e. of μ, of, and 02. (b) Find the asymptotic variance of μ.