Question

In: Statistics and Probability

Let (Un, U, n>1) be asequence of random variables such that Un and U are independent,...

Let (Un, U, n>1) be asequence of random variables such that Un and U are independent, Un is N(0, 1+1/n), and U is N(0,1), for each n≥1.

Calculate p(n)=P(|Un-U|<e), for all e>0.

Please give details as much as possible

Expert Solution

Given: and that they are independent. Hence is also normally distributed.

Let

So, .

We want:

I did all the above manipulation because . Now we can write the probabilities in terms of the standard normal distribution .

Here is the CDF of the standard normal distribution Z.

orchestra answered 2 years ago

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