2 Let be the interval 0 1 and let probabilities of subinterv

2. Let be the interval (0, 1) and let probabilities of subintervals of n be given by integrating the density function f(x) 4x3. Find the probabilities of the following subintervals a. (.2, .3) b. (.7, .8) c. [.5, .8] d. (0, .5]

Solution

Integral ( 4x^3) dx

= x^4

a) (0.2,0.3) = ((0.3)^4 - (0.2)^4) = 0.0065 Answer

b) (0.7,0.8) = ((0.8)^4 - (0.7)^4) = 0.1695 Answer

c) [0.5 ,0.8] = ((0.8)^4 - (0.5)^4) = 0.3471 Answer

d) (0,0.5] = ((0.5)^4 - (0)^4) = 0.0625 Answer