MS-Sol-EE-C14

# MS-Sol-EE-C14 - CHAPTER 14 DISCRETE PROBABILITY...

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Unformatted text preview: CHAPTER 14 DISCRETE PROBABILITY DISTRIBUTIONS EXERCISE 14.1 Section 14.1 Random variables (page 291) 1. (a) The number X of industrial accidents per year is discrete. The possible values are 0, 1, 2, 3, . . . . (b) The length of time Y to type 1 000 words is continuous. The range is (0, ∞ ). (c) The number Z of flaws in 1 m 2 of cloth is discrete. The possible values are 0, 1, 2, 3, . . . . (d) The amount T of oxygen produced in a chemical reaction is continuous. (The amount is any volume within certain range.) 2. (a) P is continuous. (b) M is discrete. (c) U is discrete. (d) V is continuous. 3. (a) P is discrete. Its range is {0, 1, 2, 3, . . . }. (b) T is continuous. Its range is [0, ∞ ). 4. (a) N is discrete. Depending on the size and complexity of the model, N can assume values 1, 2, 3, … (b) W is continuous. Depending on the size and complexity of the model, W can assume values in the interval 0 < W < ∞ . 5. (a) The range of P = {0, 0.02, 0.04, 0.06, . . . , 0.98, 1} (b) The range of G = {1, 2, 3, 4, . . . } 6. (a) X can assume values 0, 1 and 2. 166 C HAPTER 14 D ISCRETE P ROBABILITY D ISTRIBUTIONS (b) Let the sample points be denoted by ( NN ), ( NY ), ( YN ) and ( YY ), where N represents a “no” response and Y a “yes” response. The first letter represents the response of one of the two pedestrians and the second letter represents the response of the other pedestrian. The following table gives the probabilities associated with the various values of X . Sample point Value of X Probability ( NN ) 9 4 3 2 2 = ( NY ), ( YN ) 1 9 4 3 2 3 1 3 1 3 2 = + ( YY ) 2 9 1 3 1 2 = 7. (a) T can assume values 1.5, 2.5 and 3. (b) P( T > 2) = P( T = 2.5 or 3) = P( T = 2.5) + P( T = 3) Addition rule for mutually exclusive events = 3 of out stamps 2 selecting of ways of No. stamps \$2 and \$0.5 the selecting of ways of No. 3 of out stamps 2 selecting of ways of No. stamps \$2 and \$1 the selecting of ways of No. + = 3 2 3 2 1 1 C C + = 3 2 8. (a) The sample space is { HHHH , HHHT , HHTH , HTHH , THHH , HHTT , HTHT , HTTH , { THHT , THTH , TTHH , HTTT , THTT , TTHT , TTTH , TTTT }. (b) (i) X ( e ) = TTTT e TTTH TTHT THTT HTTT e TTHH THTH THHT HTTH HTHT HHTT e THHH HTHH HHTH HHHT e HHHH e = for 0, , , , = for 1, , , , , , = for 2, , , , = for 3, = for 4, (ii) x 1 2 3 4 P( X = x ) 1 16 4 16 6 16 4 16 1 16 9. (a) The range of D is {- 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5}. (b) Let ( x , y ) denote the outcome with the green die scoring x and the red die scoring y. (i) The outcomes for the event D = 3 are: (4, 1), (5, 2), (6, 3)....
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MS-Sol-EE-C14 - CHAPTER 14 DISCRETE PROBABILITY...

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