3. If X;~N(0,1), i = 1,2,3,4 are independent Normal random variables and Y is given as Y =(X,+ X;)' +(X;+ X ,)'. If aY~x², , find the constant a.

Q: Suppose that the bivariate random variable W = (W1,W2)™ has a Gaussian distribution on R² with zero…

A: Given that the bivariate random variable W=W1, W2T has a Gaussian distribution on ℝ2 with zero mean…

Q: 4. (a) Consider a nonnegative, integer valued random variable Y, and a random sample X1, ·.. , Xn.…

A: Expectation gives the most likely value of a random variable.

Q: 5. Suppose random observations Y₁ and Y₂ are independent each distributed N(0,1). Also let the…

A: It is given that  and  are independent random variable each is distributed normally with mean 0 and…

Q: 3.) Find P (X > Y) where X and Y are independent random variables that satisfy X~ N (2,1) and Y~ N…

A: We have given the following statement.

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.