please show work so the concepts can be understoodSolutionCu

please show work so the concepts can be understood

Cumulative density function

F(x) = c/x^6, x>2

Hence by total prob axiom

F(inf) -F(2) = 1

As this is ridiculous let us assume tht F is pdf.

Integral of from 2to inf = 5c/32 =1

c= 32/5

------------------------------------------

ii)

Cumulative Function for x is = int 2 to x of dx

= 1-32/5x^5

P(2

iii) Std dev

E(X^2) = integral of c/x^4 dx = 3c/2^3 = 24

E(X) = integral of c/x^5 dx = 4c/2^4 = 1.6

Var(X) = 24-2.56= 21.44

std dev (X)=4.63

-----------------------

iv)95th percentile

cum prob = 0.95

i.e. 1-32/5x^5 = 0.95

0.05(5x^5) = 32

x^5 = 128

x = 2.63