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A sample of n independent observations are obtained of a random variable having a Poisson distribution with mean . Show that the maximum likelihood estimate of is he sample mean show that the corresponding estimator is an unbiased estimator of , and has variance .
The scientists Rutherford and Geiger reported an experiment in which they counted the number of alpha particles emitted from a radioactive source during intervals of 7.5 seconds duration, for 2612 different intervals. A total of 10126 particles were counted. The data obtained are summarised in the below.
Number 0 1 2 3 4 5 6 7 8 9 10 11 12 >12 Total
Frequency 57 203 383 525 532 408 273 139 49 27 10 4 2 0 2612
It has been suggested that the number of particles emitted in a n interval may be adequately modelled by a Poisson distribution. Assuming this conjecture to be correct, find the maximum likelihood estimate of the mean of this distribution, and use this to estimate the expected frequencies corresponding to the observed frequencies given in the table. Comment informally on the extent of agreement between these observed and expected frequencies.
Attachment:- statistics 1.doc
Best Electronics, Inc. offers a "no hassle" returns policy. The number of items returned per day follows the normal distribution. The mean number of customer returns is 10.4 per day and the standard deviation is 2.3 per day.
Assume rivets are defective independently of one another, each with the same probability. If 24% of all seams need reworking, determine the probability that rivet is defective?
You were hired to do the development work for the local high school. The school has asked you to create a program to store quiz grades for the students of a class.
White blood cell counts for a group of volunteers before being innoculated, and white blood cell counts for a second group of volunteers after being innoculated.
The demand for a product of Carolina Industries varies greatly from month to month. Based on the past 2 years of data, the following probability distribution shows the company's monthly demand.
This is a quantitative analysis paper that looks at statistical data and evaluates the results. What are you trying to find? Where did you find your data? How did you get your data?
find the following z-scores for the standard normal distribution. round to three decimal places.1. z0.152.
Find the probability that a randomly selected bolt can be used (either immediately or after being cut). Find the probability that fewer than 15 out of 20 bolts can be used.
Suppose that a model for the joint distribution of these rvs is a bivariate normal distribution.
The mean amount of life insurance per household in the United States is $110,000. What is the likelihood of selecting a sample with a mean of at least $112,000?
The problem related to Basic Statistics and it discuss about calculation of mean, median and mode for the above given data
What are the characteristics of standard normal distribution? The HR department of an organization collects data on employees' age, salary, level of education, gender, and ethnicity. Which data do you think is more likely to follow normal distribu..
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