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