Math  /  Data & Statistics

Question22. Let XX denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of XX is f(x,θ)={(θ+1)xθ0x10 otherwise f(x, \theta)=\left\{\begin{array}{cl} (\theta+1) x^{\theta} & 0 \leq x \leq 1 \\ 0 & \text { otherwise } \end{array}\right. where 1<0-1<0. A random sample of ten students yields data x1=.92,x2=.79,x3=90,x4=.65x_{1}=.92, x_{2}=.79, x_{3}=90, x_{4}=.65, x5=.86,x6=.47,x7=.73,x4=.97,x9=.94x_{5}=.86, x_{6}=.47, x_{7}=.73, x_{4}=.97, x_{9}=.94, x10=.77x_{10}=.77 。 a. Use the method of moments to obtain an estimator of θ\theta and then compute the estimate for this data.

Studdy Solution
Compute the estimate of θ\theta using the sample data:
The estimate of θ\theta is 3\boxed{3}.

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