. Random Variable and Mathematical Expectation Exercise . . P X k £ .
. . . F for for for < ≤ < ≤ < for for x ≤ < ≥ .
X = x P ( X = x ) . (i) / , (ii) / , / , / (iii) . Hint: f x dx f x dx f x dx f x dx . ( ) , ( ) ( ) ) , i k ii f x < ≤ .
A i e ii e iii e ,( ) ,( ) ,( . ( ) a yes f x for x for for for for x < ≤< ≤< ≤< ≥ ( )( ) ,( ) ,( b i ii iii Exercise . . .
Expectation: ` ; Variance: ` , , ; Standard Deviation: ` , . . (or , miles) . Expectation: ; Variance: .
Exercise . (c) (d) (b) (c) (b) (c) (d) (d) (d) (d) (d) (a) (c) (c) (a) (b) (b) (a) (d) (b) (b) (c) (c) (a) (b) (c) (b) (b) (b) (b) Miscellaneous problems . (i) ½ (ii) ¼ (iii) ½ (iv) ¾ . (a) (i) / (ii) (b) X is NOT discrete since F is not a step function.
XII Std - Business Maths & Stat EM - - . ; . (a) (b) . (i) (ii) .