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Q53Section DA (Data Science and Artificial Intelligence (Q11–Q65))53 of 65

Distributional results for sums of squared standard normal variables

Let X1,X2,…,XnX_1,X_2, … ,X_n be nn independent random variables. Each of the random variables follows Normal(μ=0,σ2=1)Normal(\mu = 0, \sigma^2 = 1) distribution. Define Xˉ=1n∑i=1nXi\bar{X} = \frac{1}{n}\sum_{i=1}^{n} X_i. Which of the following statements is/are correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Options

Select every correct option, then submit.