Probability Mass Functions Notes for MTH 514, Lecture notes of Probability and Stochastic Processes

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2:2 Probability Mass Functions Ber nouls PME: P Ux) 2 P *= 0 U7 P xe \ 8) otherwise e. heods TS xz0 tals is y= \ eta+ ppl 2 Plol+P Lys! “ 2 Binomial Reandow Naviable. pat® = eLepels fave" tip [poy --> ? , be B.q the Probab ity of atthe heads k sles) Con be useck wf thes Geometric Random Vort alle we plied = (\7P) a ey wn of Wo tecges needed for, head to come up Pret. Farsson Banc om Vortable pels ©*g™ wor. ww «alah (4-EL*I)’ pt) Ere EL vs QELX +e VIN) seeds) val Ge | EID CELA 2.5 Joint PMFs of Random Variables Poy tee HOR =|» | yy? “= ) =o x Fit 4 = Pay boy Pyly? Be Pay 4) Joint PME Px y 4) tn tebWoar Torn A 4 ie} 'fr0|Yr6e Vag }-—> oe en vy (2\ 27/20 3 | ize] 7/20} A.| (fel -— Yeo £o)- 8/20 2 Yao Ee he “ye > Zao \ ho Yao Vow 6 > 3/20 . 2a | all iy can 3 yo ofzeo 8/aw Yao Othe th, zaxe2y eo 24, Hh. Yow yen Va typ Yao ‘ro 7 . Yeo Yeo Yoo 0 1 2 3 4