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Discrete PMFCDF BP Soln - 3:74 é/é a n e a.—-—_u—...

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Unformatted text preview: 3:74 é/é') a. n e a. -.—-------—--_u— MA206 - Probability 18: Statistics Lesson 19: Discrete Random Variables, PMF, CDF 1. Effective employment of deer management techniques has ensured that this year’s buck population on West Point' 1s of excellent quality. West Point’ 5 biologist has determined that the population of books, with respect to the number of points on their antlers, 1s as follows: mm--EI-E--E-I.lfil 11 ---III 2“ -----IIIIZEI a. Letting X denote the number of antler points on a given buck, construct the PMF of X using the following table: ll---']n---'I-- MMMMIM b. Determine the probability that the number of points on a randomly selected buck 15 at least 10. POE/o) :: Pm +p0r) +9021) +903)+p0q):,/9’/$ c. Determine that probability that the number of points on a randomly selected buck is between 4 and 8 (inclusive). Pct/:2 Y5: 3’) 3 PM W“) +103) ”’57) ”(5’) 1153917 d. Determine the probability that the number of points on a randomly selected buck 1s less than 3 P On: 3) :- ‘pCO + (201) =— J5" e. How would you calculate the “expected” number of points on a randomly selected buck? (£1170 bra/.- 55y): My; 2 X‘EFCX) : d) C-OG‘H 3(:/)[email protected])7h., —_- 6‘ 31/3 fidfnta‘? - 1 ' 8— -12 4 5 2. A discrete random variable has a PMF of the fol-m p=(x) {a x) for x- ”3 ............... otherwise :1. Find the constant c. . 7 L) .2” 1:63-90:1/ - C. 2(9 x): (If/*2 N” W (=1 . .: gen (3* (7+€+J‘+‘/+33‘V/ .. C M I 7:1: 13. Find the CDF, F(x). ‘ >12: / c. Find P(X:=- 3). .1 p C415 + p 6:?) 3 534? or using cox: 1f 15(3)”: l] .,;,y d. FindP(2£X<:5). : P00 + Pg.) 7179693, {0 , 0r“ (/J/Pts CUP 0: 0/) ‘— F (2-) = F6?) "F0) :. 35—. at to 3. A stockroorn clerk returns three safety helmets at random to three coal miners who had previously checked them If Smith, Jones, and Brown in that order, receive one of the three hats, complete the following. a. Identify all the possible orders of returning the helmets. {5.) ”:33 (Eire a; (0;: J5 (5.153 (1393,53 b. Let the random variable M stand for the number of correct matches. List its possible valuesm. €§)J,GS ~—-_. 3 Cairns-72'" EEJJI‘F; 4/ (3:“, as; as; l. _ ELLE-3% / {535;43 __~.,..o {JJBJJE—l“ ‘3’ c. Create the PMF for M. d. Create the GDP for M. ...
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