Question

7:02 X homework on exponential distribut... ... for exponential They claic that O Homework distriestin A firm melies heat lours. the lifetime of the bulb is 10h. We want to test this claim. we suppose Hat the lifetime of the bull is exponential are 210 (meerusid on Louis a, we leer testing Insing the bulbs one after the other. What is the probability of the e thel He wlica web en He wc hesap b., we keep testing until we find 3 bulls i les k e fetime the low what is the probability that this happen when testing the fath ball.? on what to the expected tuted lifetiment of , . d. 3 we test 12 bulbs wheat is the probability that more Haan 2 of the has a lifetime shorter then : 9 hours.

Answer 1

VIASSmat Date page- X: lifetime of bulb An exponental (mean=lo) وجعل = (ع) @ Probability C exactly 4th buth I is first bulb with lifetime . less than lola للمدع)) ((0_PX) (3) - Negative binomial PCX Lio) as success طعم ين له همسر نمر : اها 8 ) - ( ۶۱۰ ها

ge classmate Date Page e et zire PCX>10) . 1- Pc X Lio) - a -liret) Pcx>10) = é bulb me Probability required = (le) ce') = (he) = 0.0315 Probability c finding exactly 3rd bulb's lifetime shooter than 10 while testing sth bulb) -(7.) (Pexsto) js RX2013 (76) (e) cl-e") 0.0357

classmate Date page total - Expected a lifetime of 8 bulbs expected lifchine of for bulb ta expected lifetime of the bulle lot.... To 8 xlo دف Probability (out of a bulb I more than 2 has lifetime shorker man to) 7 for Binomial where PCX clo) ist - Pex 710.) is I-P no 12 1- (12) (8° (1-P)12 - 12 17-p" - 112742 (p) ( 2 ) - (61) 12 - 12x (1-0) Celt

Date Page ای ) (تم) ع کی ۔ ہا + 12x11-et le 1- eto Le 2 ھ - 66C ( - e + 374 و 32 - 0 + 3.Coے ۔ يقو3-6 66 + ی231.م + 35ه)°ے 26. 36 * (کو 3 .2 ) •اح - ا - دا د ن . - ک هو ده .