Question

The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by

fX(x) = ( C/x^2 x>5

0 x<5

where C>0 is a constant which needs to be determined.

(i) What is the probability that the device’s lifetime is 10 hours?

(ii) Find the 25%th quantile of X?

(iii) If the device lifetime is X, then its total electricity cost equals . What is the expected total electricity cost of the device?

Answer 1

Answeos &x 100 = C 275 o ; 0.60 1) value of ca dx = 1 7 (7) 3 ( [04:31 = c():1

10.2) 25:/. Quontile = TSF quootile AG: ECG F(xs92 g food로 영 v1 [주] - +16-] E_ Te 1 G+ 16- ㅋ - +5 4 - ㅋ gt555 |ㅋ 9: 20-5 = 15 = 375 La년

9.3) E(X)= ŕ x.frx) dx dx, = r 5 da 27 7, = 5 5 1 dx .. 5 [109x15 = 5 [10900 - 1095) = 5 [O-1.6094] E(x) = le does not exists, Foo ci) → poobability that the device's lifetime is lo hours is zedo. Because for continous Bli ghaibution Doobability at a point is always_zero.