168 | |
177 | |
194 | |
169 | |
159 | |
172 | |
174 | |
177 | |
159 | |
172 | |
181 | |
171 | |
168 | |
162 | |
168 | |
157 | |
180 | |
174 | |
162 | |
177 | |
mean | 171.05 |
variance | 79.73421 |
maximum | 194 |
median | 171.5 |
a)
form normal distribution
sample mean and sample variance are MLE for and
MLE of = 171.05
MLE of = 79.73421
b),
for Uniform distribution
MLE for is Max(X1,X2,...Xn)
= 194
c)
for double exponential distribution
MLE of is Median = 171.5
3. This problem is concerned with the maximum likelihood estimate (MLE) of various distributions. Bob, Céline...
Concept Check: Terminology 0/3 points (graded) Suppose you observe iid samples X1,…,Xn∼P from some unknown distribution P. Let F denote a parametric family of probability distributions (for example, F could be the family of normal distributions {N(μ,σ2)}μ∈R,σ2>0). In the topic of goodness of fit testing, our goal is to answer the question "Does P belong to the family F, or is P any distribution outside of F ?" Parametric hypothesis testing is a particular case of goodness of fit testing...