Question:
Suppose that the lifetimes (in months) of bulbs manufactured by a company have an \( \text{Exp}(\lambda) \) distribution, where \( \lambda > 0 \). A random sample of size 10 taken from the bulbs manufactured by the company yields the sample mean lifetime \( \bar{x} = 3.52 \) months. Then the uniformly minimum variance unbiased estimate of \( \frac{1}{\lambda} \) based on this sample is equal to __________ months (round off to 2 decimal places).
Suppose that the lifetimes (in months) of bulbs manufactured by a company have an \( \text{Exp}(\lambda) \) distribution, where \( \lambda > 0 \). A random sample of size 10 taken from the bulbs manufactured by the company yields the sample mean lifetime \( \bar{x} = 3.52 \) months. Then the uniformly minimum variance unbiased estimate of \( \frac{1}{\lambda} \) based on this sample is equal to __________ months (round off to 2 decimal places).
Updated On: Oct 1, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 3.5 - 3.55
Solution and Explanation
The correct Answer is : 3.50 -3.55(Approx.)
Was this answer helpful?
0
0
Top Questions on Estimation
- A biased coin, with probability of head as \( p \), is tossed \( m \) times independently. It is known that \( p \in \left\{ \frac{1}{4}, \frac{3}{4} \right\} \) and \( m \in \{3, 5\}. \) If 3 heads are observed in these \( m \) tosses, then which of the following statements is correct?
- IIT JAM MS - 2024
- Statistics
- Estimation
- Let \( X_1, X_2, \ldots, X_{10} \) be a random sample from a \( U(-\theta, \theta) \) distribution, where \( \theta \in (0, \infty) \). Let \( X_{(10)} = \max \{ X_1, X_2, \ldots, X_{10} \} \) and \( X_{(1)} = \min \{ X_1, X_2, \ldots, X_{10} \} \). If the observed values of \( X_{(10)} \) and \( X_{(1)} \) are 8 and -10, respectively, then the maximum likelihood estimate of \( \theta \) is equal to __________ (answer in integer).
- IIT JAM MS - 2024
- Statistics
- Estimation
- A year is chosen at random from the set of years {2012, 2013, β¦ , 2021}. From the chosen year, a month is chosen at random and from the chosen month, a day is chosen at random. Given that the chosen day is the 29th of a month, the conditional probability that the chosen month is February equals
- IIT JAM MS - 2022
- Statistics
- Estimation
- In a store, the daily demand for milk (in litres) is a random variable having Exp(Ξ») distribution, where Ξ» > 0. At the beginning of the day, the store purchases c (> 0) litres of milk at a fixed price b (> 0) per litre. The milk is then sold to the customers at a fixed price s (> b) per litre. At the end of the day, the unsold milk is discarded. Then the value of c that maximizes the expected net profit for the store equals
- IIT JAM MS - 2022
- Statistics
- Estimation
- Let 0.2, 1.2, 1.4, 0.3, 0.9, 0.7 be the observed values of a random sample of size 6 from a continuous distribution with the probability density function
\(f(x) = \begin{cases} 1, & 0< x \le \frac{1}{2} \\ \frac{1}{2\theta-1}, & \frac{1}{2} \lt x \le \theta \\ 0, & \text{otherwise,}\end{cases}\)
where ΞΈ > \(\frac{1}{2}\) is unknown. Then the maximum likelihood estimate and the method of moments estimate of ΞΈ, respectively, are- IIT JAM MS - 2022
- Statistics
- Estimation
View More Questions
Questions Asked in IIT JAM MS exam
- A bag has 5 blue balls and 15 red balls. Three balls are drawn at random from the bag simultaneously. Then the probability that none of the chosen balls is blue equals
- IIT JAM MS - 2024
- Probability
- Let the random vector \( (X, Y) \) have the joint probability density function
\[f(x, y) = \begin{cases} \frac{1}{x}, & \text{if } 0 < y < x < 1 \\0, & \text{otherwise} \end{cases}.\]
Then \( \text{Cov}(X, Y) \) is equal to:- IIT JAM MS - 2024
- Probability
- Two factories \( F_1 \) and \( F_2 \) produce cricket bats that are labelled. Any randomly chosen bat produced by factory \( F_1 \) is defective with probability 0.5 and any randomly chosen bat produced by factory \( F_2 \) is defective with probability 0.1. One of the factories is chosen at random, and two bats are randomly purchased from the chosen factory. Let the labels on these purchased bats be \( B_1 \) and \( B_2 \). If \( B_1 \) is found to be defective, then the conditional probability that \( B_2 \) is also defective is equal to __________ (round off to 2 decimal places).
- IIT JAM MS - 2024
- Probability
- Consider a coin for which the probability of obtaining head in a single toss is \( \frac{1}{3} \). Sunita tosses the coin once. If head appears, she receives a random amount of \( X \) rupees, where \( X \) has the \( \text{Exp}\left( \frac{1}{9} \right) \) distribution. If tail appears, she loses a random amount of \( Y \) rupees, where \( Y \) has the \( \text{Exp}\left( \frac{1}{3} \right) \) distribution. Her expected gain (in rupees) is equal to __________ (answer in integer).
- IIT JAM MS - 2024
- Probability
- If 12 fair dice are independently rolled, then the probability of obtaining at least two sixes is equal to __________ (round off to 2 decimal places)
- IIT JAM MS - 2024
- Probability
View More Questions