Parameter Estimation

Parameter Estimation is a branch of statistics that involves using sample data to estimate the parameters of a distribution.

Some distributions and their parameters:

Distribution	Parameters (θ)
Bernoulli(p)	θ = p
Poisson(λ)	θ = λ
Uniform(a, b)	θ = [a, b]
Normal(μ, σ^2)	θ = [μ, σ^2]

Task

1. Let (𝑋1, 𝑋2,…,)be a random sample of size n taken from a Normal Population with parameters: mean= 𝜃1 and variance=𝜃2. Find the Maximum Likelihood Estimates of these two parameters.
2. Let X_1, X_2 . . . ,X_n be a random sample from B(m, θ) distribution, where θ ∈Θ =(0, 1) is unknown and ‘m’ is a known positive integer. Compute value of θ using the M.L.E.

Submitted by:

• Rohan Thakur (102103762)