Show me as much as you can about what you do understand conc

Show me as much as you can about what you do understand concerning a problem whether or not you think you can completely solve it. Consider the continuous random variable X with pdf f(x) = x/8 for 0 le x le 4

Solution

Total prob must be 1

integral of x/8 dx = x^2/16 = 1

Hence pdf

E(X) = integral of x f(x) dx

= x^3/24

= 64/24 = 8/3

E(x^2) = integral of x^2 f(x) dx

= x^4/32

=8

Hence var = 8-64/9 = 8/9

d) CDF - 0 to x integral f(x) dx

= x^2/16, 0<x<4

e) Median is when cdf = 0.5

Or x = 2 rt 2