My Norss Aak Your Taach A new battery\'s vu tdge \'ndy be deep d e A or undecep

Question

My Norss Aak Your Taach A new battery's vu tdge 'ndy be deep d e A or undecep d le U . A or dm nd lí hl requ 'es t u bauenes, su bd e e s will be "Jep Let Y denote the nuiber of betteries that must be tested. den y selected dnd tested until 0 dnep d ve "es have been found Suppuse Inal, 93% of all battenes h ve duce lable vultdues. a) What is p(2), that is PY 2)7 (Round your answar to four dacimal places.) (b) what is p(3)? [Hint: There are two different outcomes that result in -3]. (Round your answer to three decimal places.) p(3)-10.1200 Tu heve5, whel tnust be true of Uhe nifth bellery seleteJ? The fifth battary must ba an A The nrth battery must b U. List the four outcomes for which -5. (Enter your ¡ver in set notation. Detarmine ) Round your answer to five decimal places.) (5)-10.00119 d Use the pattern in your answers or parts (-)to obtain a general ormula for py) p(y) _ (y-1 k 1°0.93 %0.07-2) X Your answer cannot be understood or graded. Mre Information Need Help? RTalk to a Tutor

Explanation / Answer

Y follows negative binomial distribution

the negative binomial distribution is a discrete probability distribution of the number of successes in a sequence of independent and identically distributed Bernoulli trials before a specified (non-random) number of failures (denoted r) occurs.

here we need 2 success in total

last should be success and for (y-1) number of success = 1

P(Y = y) = (y-1)C1 * (1-p)^(y-2) * p * p

= (y-1) * p^2 * (1-p)^(y-2)

= (y-1) * 0.07^(y-2) * 0.93^2

Note that don't put C in answer. simplify it nC1 = n

hence

(y-1) * 0.07^(y-2) * 0.93^2

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