A geometric distribution is a special case of a negative binomial distribution with \(r=1\).

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>> >> /Encoding 21 0 R /BaseFont/UXPPJJ+CMSY8 /Type/Encoding The experiment should be of x …

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>> /FontDescriptor 23 0 R /FontDescriptor 19 0 R Assume Bernoulli trials — that is, (1) there are two possible outcomes, (2) the trials are independent, and (3) \(p\), the probability of success, remains the same from trial to trial. 295.1 826.4 531.3 826.4 531.3 559.7 795.8 801.4 757.3 871.7 778.7 672.4 827.9 872.8 /Differences[0/minus/periodcentered/multiply/asteriskmath/divide/diamondmath/plusminus/minusplus/circleplus/circleminus/circlemultiply/circledivide/circledot/circlecopyrt/openbullet/bullet/equivasymptotic/equivalence/reflexsubset/reflexsuperset/lessequal/greaterequal/precedesequal/followsequal/similar/approxequal/propersubset/propersuperset/lessmuch/greatermuch/precedes/follows/arrowleft/arrowright/arrowup/arrowdown/arrowboth/arrownortheast/arrowsoutheast/similarequal/arrowdblleft/arrowdblright/arrowdblup/arrowdbldown/arrowdblboth/arrownorthwest/arrowsouthwest/proportional/prime/infinity/element/owner/triangle/triangleinv/negationslash/mapsto/universal/existential/logicalnot/emptyset/Rfractur/Ifractur/latticetop/perpendicular/aleph/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/Q/R/S/T/U/V/W/X/Y/Z/union/intersection/unionmulti/logicaland/logicalor/turnstileleft/turnstileright/floorleft/floorright/ceilingleft/ceilingright/braceleft/braceright/angbracketleft/angbracketright/bar/bardbl/arrowbothv/arrowdblbothv/backslash/wreathproduct/radical/coproduct/nabla/integral/unionsq/intersectionsq/subsetsqequal/supersetsqequal/section/dagger/daggerdbl/paragraph/club/diamond/heart/spade/arrowleft 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 14 0 obj

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Now, let \(X\) denote the number of people he selects until he finds \(r=3\) who attended the last home football game.

stream A representative from the National Football League's Marketing Division randomly selects people on a random street in Kansas City, Kansas until he finds a person who attended the last home football game. /Widths[1062.5 531.3 531.3 1062.5 1062.5 1062.5 826.4 1062.5 1062.5 649.3 649.3 1062.5

/Type/Font Let \(p\), the probability that he succeeds in finding such a person, equal 0.20. Any specific negative binomial distribution depends on the value of the parameter \(p\).

875 531.2 531.2 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 708.3 708.3 826.4 826.4 472.2 472.2 472.2 649.3 826.4 826.4 826.4 826.4 0 0 0 0 0 492.9 510.4 505.6 612.3 361.7 429.7 553.2 317.1 939.8 644.7 513.5 534.8 474.4 479.5 462.4 761.6 734 693.4 707.2 747.8 666.2 639 768.3 734 353.2 503 761.2 611.8 897.2 /Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5

>>

<< /Name/F2 (Are you growing weary of this example yet?) endobj 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 489.6 272 272 761.6 489.6 /Subtype/Type1 Following are the key points to be noted about a negative binomial experiment.

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Example 3: Negative Binomial Quantile Function (qnbinom Function) Similar to the R syntax of Examples 1 and 2, we can create a plot containing the negative binomial quantile function. endobj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 606.7 816 748.3 679.6 728.7 811.3 765.8 571.2

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