IITM BS Question 31 - Week 7 Practice

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IITM BS Question 31 - Week 7 Practice | Prasnya

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Q31Comprehension3 Marks24 Dec 2023

Passage

Based on the above data, answer the given subquestions. The probability density function of a continuous random variable

X

is given by

f_X(x, \alpha) = \begin{cases} \alpha^{-2} x e^{-x / \alpha}, & x > 0, \alpha > 0 \\ 0, & \text{otherwise} \end{cases}

Hint:

\int_0^\infty \frac{x^k}{\theta} e^{-x/\theta} dx = k! \theta^k

Let a random sample of

X

6, 7.5, 7.5, 3, 6

. Find the maximum likelihood estimate of

\alpha

for the given sample.

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Q31

00:00

24 Dec 2023

Statistics 2 · Week 7

Q31.Let a random sample of

X

6, 7.5, 7.5, 3, 6

. Find the maximum likelihood estimate of

\alpha

for the given sample.@passage

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