Discuss the below:
Q: Let X denote the proportion of alloted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is
f(x,θ)={(θ+1)xθ 0<=x<=1
0 otherwise
where -1<θ. A random sample of ten students yields data x1=0.92, x2=0.79,x3=.90, x4=.65 , x5=.86,x6=.47, x7=.73,x8=.97,x0=.94.x10=.77
a. Use method of moments to obtain an estimator θ then compute the estimate for this data.
b. Obtain the maximum likelihood esitmator θ and then compute the estimate for the given data.