Question

SENARASURA Let X denote the amount of space occupied by an artide placed in a 1-ftpacking container. The pdf of X is below. - -) 0<x< 1 O therwise (a) Graph the pat 0.2 04 06 08 10 02 0.4 0.6 0.8 1. 02 010 0.4 0.6 0.8 1.0 Obtain the cef of x.

Answer 1

We need to find probability P[ X > $\mu$ + $\sigma$  ] = P[ X > 0.81818 + 0.11134 ] = P[ X > 0.92952 ]

Given,

mean(x) = $\mu$ = 0.81818

standard deviation = $\sigma$ = 0.11134

To calculate P[ X > 0.92952 ] we need to see the value of CDF between X less than 1 and greater than 0

F(x) = P[ X > x] = x^9*( 10 - 9*x)

Here, x = 0.92952

P[ X > 0.92952 ] = 0.92952^9*( 10 - 9*0.92952 )

P[ X > 0.92952 ] = 0.517998*( 10 - 8.36568‬ )

P[ X > 0.92952 ] = 0.517998*1.63432

P[ X > 0.92952 ] = 0.84657449

P[ X > 0.92952 ] = 0.8466 ( rounding to 4 decimal place )