Reference no: EM13867264

Let an applicationdefined for all , by:

Where  and 

1-      Determine kas a function of such that  is the probability density function of a random variable X.

2-      What is the distribution function of X?

3-      If we defined  . What is the distribution of ?

4-      Calculate E(X) and V(X)

5-      Evaluate P (| Y | ≥ 2). Compare with P (| U | ≥ 2) where successively follows a distribution  N (0, 1), a distribution of Student at 20 degrees of freedom, a Cauchy distribution ofdensity   , a double exponential  distribution of density

Attachment:- What is the distribution function of X.docx