[※]Confidence interval

[393sh]

Question：

So I have a little bit confuse about the sentence”Suggest a suitable estimate of the variance“.
My understanding : CI = 95 % ->α = 5%; sample ~ a half normal distribution -> μ = the mean of x
so to estimate μ and δ^2 unknown using t distrbution
Could you please help me analysis and list the relevant equations？

 

[BigBeachBanana]

View attachment 31755
Question：
View attachment 31756
So I have a little bit confuse about the sentence”Suggest a suitable estimate of the variance“.
My understanding : CI = 95 % ->α = 5%; sample ~ a half normal distribution -> μ = the mean of x
so to estimate μ and δ^2 unknown using t distrbution
Could you please help me analysis and list the relevant equations？

Have you learned about the maximum likelihood estimator?

 

[393sh]

yes，could you help me check my answer right or not and correct my mistake？

 

[BigBeachBanana]

yes，could you help me check my answer right or not and correct my mistake？
View attachment 31772

The maximum likelihood of the half-normal distribution is [math]\hat{\theta}=\sqrt{\frac{\sum_{i=1}^{n}x_i^2}{n}}[/math]However, this would require you to have the raw data or know [imath]\sum_{i=1}^{n}x_i^2[/imath]. I'm not sure if this information was given/computed in previous questions. However, I don't see why your method would be invalid.

 

[393sh]

The maximum likelihood of the half-normal distribution is [math]\hat{\theta}=\sqrt{\frac{\sum_{i=1}^{n}x_i^2}{n}}[/math]However, this would require you to have the raw data or know [imath]\sum_{i=1}^{n}x_i^2[/imath]. I'm not sure if this information was given/computed in previous questions. However, I don't see why your method would be invalid.

this is previous question but I think question (e) is independent one and I wanne to learn how to solve question (e)

 

[BigBeachBanana]

this is previous question but I think question (e) is independent one and I wanne to learn how to solve question (e)
View attachment 31774

The previous questions are theoretical, whereas (e) requires a numerical answer. So the actual value of [imath]\sum_{i=1}^{n}Y_i^2[/imath] was not given, therefore we can't use the likelihood estimator. I think your method is fine.

 

[393sh]

OK thank you so much

The previous questions are theoretical, whereas (e) requires a numerical answer. So the actual value of [imath]\sum_{i=1}^{n}Y_i^2[/imath] was not given, therefore we can't use the likelihood estimator. I think your method is fine.