10. Let Y₁, Y₂,..., Yn be a random sample of size n from a gamma distribution withparameters and a both being 1. Is Y a pivotal quantity? Show why and whynot is a pivotal quantity.11. Consider a random sample Y₁, Y₂, ..., Yn from a normal population Y~N(u,0²)where the population variance and mean are unknown. We want to construct aΣ(X₁-X)² Show0²100(1a)% confidence interval for the population variance if:whether or not is a pivotal quantity and construct a 100(1-a) confidenceinterval.

Note: According to Bartleby guidelines expert solve only one question and rest can be reposted.

Answered: 10. Let Y₁, Y₂,..., Yn be a random…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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2. Suppose it is claimed that amongst the population of STM1001 students, the number of items bought online in the past year is normally distributed with a mean of u 20 and variance of o2 = 25. Further suppose that we wish to study the mean of the population by taking a random sample of n = 61 STM1001 students. Using this information, write down the distribution of the sample mean, X. Note: In each box, enter a single number rounded to four decimal places where relevant. (2 marks) X~ N( 20 0.4098 2 4. Again following on from the previous question, what is the probability that when we take a random sample of n = 61 STM1001 students, the sample mean would be either greater than 20.3521 or less than 19.6479? [int. orty will b own that
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10. Let Y₁, Y₂,..., Yn be a random sample of size n from a gamma distribution with parameters and a both being 1. Is Y a pivotal quantity? Show why and why not is a pivotal quantity.