EL630 HW4

EL630 HW4 - EL630: Homework 4 1. (Book: 4-9) Find f ( x) if...

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1 EL630: Homework 4 1. (Book: 4-9) Find () i f () ( 1 )( ) . x f x Fx e ux c α = −− (Hint: For any function ( ), hx we have ()( ) ()( ) , hx xa ha xa δδ −= which is called the sampling property of the impulse function.) 2. (Book: 4-10) If is (0,4) find (a) {1 2} and (b) 2| 1}. NP P ≤≤ X X XX 1 2 c x
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2 (Hint: (0,4) N means 22 ( ) /2 2 1 () 2 x fx e µσ πσ −− = X with 2 0, 2 = . Then we have {1 2} (2) (1) P FF ≤≤ = XX X . ( 2 1 ( ) ( ) ( ) 1/2 2 x y xx F x e dy G erf µµ σσ −∞ = = = X . Then use Table 4-1.) 3. (Book: 4-18) Show that ( ) ( | ) ( ) ( | )[1 ( )]. PA PA xFx PA x Fx = + >− 4. (Book: 4-19) Show that ( | ) () (| ) . x x PA xF x FxA = X 5. (Book: 4-27) A coin is tossed an infinite number of times. Show that the probability that k heads are observed at the n th toss but not earlier equals 1 . 1 n knk pq k    [See also book (4-63).] 6. (Book: 4-30) The probability that a driver will have an accident in 1 month equals 0.02. Find the probability that in 100 months he will have three accidents.
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3 7. (Book: 4-31) A fair die is rolled five times. Find the probability that “one” shows twice,
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This note was uploaded on 02/10/2012 for the course EL 6303 taught by Professor Pm during the Spring '10 term at NYU Poly.

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EL630 HW4 - EL630: Homework 4 1. (Book: 4-9) Find f ( x) if...

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