Question

A manufacturing company has developed a machine for cleaning carpet that is fuel-efficient because it delivers carpet cleaner so rapidly. Of interest is a random variable X, the amount in gallons per minute delivered. It is known that the function is given by

f(x) = (2x + 1)/20; 0<x< 4,

1. Sketch the density function.

2. Give E(X), E(X²), and Var(X)

Answer 1

) OXCez. 9/20+ 2 3 4 5

E(X) = (x. 2x+1 dair oco 2xtl 20 E I lx (2x+1) daer trove N О N 81 f(2x + x) alx [2.61-0) + $ (16-07 95 2 2.5333 ( appeara) 2

[(x)= x 2x1 1 dx 2, 22+ 20 da 112 a 112 15 2 92 V(x)=E(XY)- E'(x) = 2236 225 = 1.0489 Cappoon) E(X) = 2.5333 gallons I min E (X2) = 112/15 = 7 14 667 gallon?/min. v(x) = -0489 gallone / min.