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Probability and StatisticsQuestion and Answers: Page 6

Question Number 153405    Answers: 0   Comments: 0

Question Number 153401    Answers: 2   Comments: 1

Question Number 153399    Answers: 0   Comments: 2

Question Number 152940    Answers: 1   Comments: 0

In bottle manufacturing company, it was observed that 5% of the bottles manufactured were defective. In a random sample of 150 bottles, find probability that (a) exactly 3, (b) between 3 and 6, (c) at most 4, manufactured bottles are defective. [Take e = 2.718]

$$\:\mathrm{In}\:\mathrm{bottle}\:\mathrm{manufacturing}\:\mathrm{company},\:\mathrm{it} \\ $$$$\mathrm{was}\:\mathrm{observed}\:\mathrm{that}\:\mathrm{5\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bottles} \\ $$$$\mathrm{manufactured}\:\mathrm{were}\:\mathrm{defective}.\:\mathrm{In}\:\mathrm{a}\: \\ $$$$\mathrm{random}\:\mathrm{sample}\:\mathrm{of}\:\mathrm{150}\:\mathrm{bottles},\:\mathrm{find}\: \\ $$$$\mathrm{probability}\:\mathrm{that}\: \\ $$$$\:\left({a}\right)\:\mathrm{exactly}\:\mathrm{3}, \\ $$$$\:\left({b}\right)\:\mathrm{between}\:\mathrm{3}\:\mathrm{and}\:\mathrm{6}, \\ $$$$\:\left({c}\right)\:\mathrm{at}\:\mathrm{most}\:\mathrm{4}, \\ $$$$\:\mathrm{manufactured}\:\mathrm{bottles}\:\mathrm{are}\:\mathrm{defective}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left[\mathrm{Take}\:\:{e}\:=\:\mathrm{2}.\mathrm{718}\right] \\ $$

Question Number 152937    Answers: 1   Comments: 0

Question Number 152935    Answers: 1   Comments: 0

Question Number 152903    Answers: 5   Comments: 0

Question Number 152683    Answers: 1   Comments: 0

The probability that athlete will win a race is (1/6) and that he will be second and third are (1/4) and (1/3) respectively.what is the probability that he will not be first in the first three place! Please,help me out

$${The}\:{probability}\:{that}\:{athlete}\:{will}\:{win}\:{a}\:{race}\:{is}\:\frac{\mathrm{1}}{\mathrm{6}}\:{and}\:{that} \\ $$$${he}\:{will}\:{be}\:{second}\:{and}\:{third}\:{are}\:\frac{\mathrm{1}}{\mathrm{4}}\:{and}\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${respectively}.{what}\:{is}\:{the}\:{probability}\:{that}\:{he}\:{will}\:{not}\:{be}\:{first} \\ $$$${in}\:{the}\:{first}\:{three}\:{place}! \\ $$$${Please},{help}\:{me}\:{out} \\ $$

Question Number 152321    Answers: 0   Comments: 0

Question Number 151602    Answers: 6   Comments: 0

Question Number 151454    Answers: 0   Comments: 2

when a die is rolled 42 times it is so happened that a face having the digit i times occured 2i times. then find the mean deviation from the mean of this discrete frequency distribution. ans is ((80)/(63)) sol pls

$${when}\:{a}\:{die}\:{is}\:{rolled}\:\mathrm{42}\:{times}\:{it}\:{is}\:{so} \\ $$$${happened}\:{that}\:{a}\:{face}\:{having}\:{the}\:{digit}\:{i} \\ $$$${times}\:{occured}\:\mathrm{2}{i}\:{times}.\:{then}\:{find}\:{the} \\ $$$${mean}\:{deviation}\:{from}\:{the}\:{mean}\:{of}\:{this} \\ $$$${discrete}\:{frequency}\:{distribution}. \\ $$$${ans}\:{is}\:\frac{\mathrm{80}}{\mathrm{63}} \\ $$$${sol}\:{pls} \\ $$

Question Number 150450    Answers: 0   Comments: 0

show the?connection between the beta distribution(n,p) and hypergeometric distribution(N,k,n)in a limiting case

$$\mathrm{show}\:\mathrm{the}?\mathrm{connection}\:\mathrm{between}\:\mathrm{the} \\ $$$$\mathrm{beta}\:\mathrm{distribution}\left(\mathrm{n},\mathrm{p}\right)\:\mathrm{and}\:\mathrm{hypergeometric} \\ $$$$\mathrm{distribution}\left(\mathrm{N},\mathrm{k},\mathrm{n}\right)\mathrm{in}\:\mathrm{a}\:\mathrm{limiting}\:\mathrm{case} \\ $$

Question Number 150323    Answers: 0   Comments: 0

a pmf of a random variable Xis given as f(x)=(e^(−10) . 10^x )/x! X=0 , 1 ,2 ... find P(x<16)

$$\mathrm{a}\:\mathrm{pmf}\:\mathrm{of}\:\mathrm{a}\:\mathrm{random}\:\mathrm{variable}\:\mathrm{Xis}\:\mathrm{given}\:\mathrm{as} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{e}^{−\mathrm{10}} .\:\mathrm{10}^{\mathrm{x}} \right)/\mathrm{x}!\:\:\mathrm{X}=\mathrm{0}\:,\:\mathrm{1}\:,\mathrm{2}\:...\:\mathrm{find}\: \\ $$$$\mathrm{P}\left(\mathrm{x}<\mathrm{16}\right) \\ $$

Question Number 150154    Answers: 0   Comments: 0

1)The probability of a Malaria patient surviving from a newly discovered drug is 0.27,while the probability of a typhoid patient surviving from another newly discovered drug is 0.85.Find the probabilities of i)Either of the two patient surviving ii)Neither of the two patient surviving iii)At least one survives

$$\left.\mathrm{1}\right)\mathrm{The}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Malaria}\:\mathrm{patient}\: \\ $$$$\mathrm{surviving}\:\mathrm{from}\:\mathrm{a}\:\mathrm{newly}\:\mathrm{discovered} \\ $$$$\mathrm{drug}\:\mathrm{is}\:\mathrm{0}.\mathrm{27},\mathrm{while}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{typhoid}\:\mathrm{patient}\:\mathrm{surviving}\:\mathrm{from}\:\mathrm{another} \\ $$$$\mathrm{newly}\:\mathrm{discovered}\:\mathrm{drug}\:\mathrm{is}\:\mathrm{0}.\mathrm{85}.\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{probabilities}\:\mathrm{of}\: \\ $$$$\left.\mathrm{i}\right)\mathrm{Either}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{patient}\:\mathrm{surviving} \\ $$$$\left.\mathrm{ii}\right)\mathrm{Neither}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{patient}\:\mathrm{surviving} \\ $$$$\left.\mathrm{iii}\right)\mathrm{At}\:\mathrm{least}\:\mathrm{one}\:\mathrm{survives} \\ $$

Question Number 150030    Answers: 0   Comments: 0

Roll a fair die twice and define A to be event that the sum of the scores showing up is greater than 7, B be the event that the sum of the scores showing up is a multiple of 3 and C be the event that the sum of the scores showing up is a prime number. Which of the events A,B and C are independent event? are the 3 events jointly independent?

$$\mathrm{Roll}\:\mathrm{a}\:\mathrm{fair}\:\mathrm{die}\:\mathrm{twice}\:\mathrm{and}\:\mathrm{define}\:\mathrm{A}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{event}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing} \\ $$$$\mathrm{up}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than}\:\mathrm{7},\:\mathrm{B}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing}\:\mathrm{up}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{multiple}\:\mathrm{of}\:\mathrm{3}\:\mathrm{and}\:\mathrm{C}\:\mathrm{be}\:\mathrm{the}\:\mathrm{event}\:\mathrm{that} \\ $$$$\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{scores}\:\mathrm{showing}\:\mathrm{up}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{prime}\:\mathrm{number}.\:\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{events}\: \\ $$$$\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{are}\:\mathrm{independent}\:\mathrm{event}? \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{3}\:\mathrm{events}\:\mathrm{jointly}\:\mathrm{independent}? \\ $$$$ \\ $$

Question Number 149981    Answers: 1   Comments: 0

a full deck of 52 cards contains 13 hearts. Pick 8 cards from the deck at random without replacement. what is the probability that you get no heart?

$$\mathrm{a}\:\mathrm{full}\:\mathrm{deck}\:\mathrm{of}\:\mathrm{52}\:\mathrm{cards}\:\mathrm{contains}\:\mathrm{13} \\ $$$$\:\mathrm{hearts}.\:\mathrm{Pick}\:\mathrm{8}\:\mathrm{cards}\:\mathrm{from}\:\mathrm{the}\:\mathrm{deck} \\ $$$$\mathrm{at}\:\mathrm{random}\:\mathrm{without}\:\mathrm{replacement}. \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{you}\:\mathrm{get} \\ $$$$\mathrm{no}\:\mathrm{heart}? \\ $$$$ \\ $$

Question Number 149534    Answers: 2   Comments: 0

Question Number 149532    Answers: 1   Comments: 0

on realise une suite infinie d′epreuves independantes.chaque epreuve resulte en un succes avec la probabilite p∈]0;1[ ou un echec avec la probabilite q=1−p.soit A_n l′evement “obenir au moins un succes au cours des premieres epreuves.” determiner P(A_n )

$${on}\:{realise}\:{une}\:{suite}\:{infinie}\:{d}'{epreuves} \\ $$$${independantes}.{chaque}\:{epreuve}\:{resulte}\:{en} \\ $$$$\left.{un}\:{succes}\:{avec}\:{la}\:{probabilite}\:{p}\in\right]\mathrm{0};\mathrm{1}\left[\:{ou}\:{un}\right. \\ $$$${echec}\:{avec}\:{la}\:{probabilite}\:{q}=\mathrm{1}−{p}.{soit}\:{A}_{{n}} \\ $$$${l}'{evement}\:``{obenir}\:{au}\:{moins}\:{un}\:{succes}\:{au} \\ $$$${cours}\:{des}\:{premieres}\:{epreuves}.''\:{determiner} \\ $$$${P}\left({A}_{{n}} \right) \\ $$

Question Number 149471    Answers: 1   Comments: 0

on distribue au hasard 8 boules b_1 ...b_8 dans 6 tiroirs t_1 ...t_6 .soit A_i l′evenement “le tiroir t_i est vide” les evenements A_1 et A_2 sont-ils independants ?

$${on}\:{distribue}\:{au}\:{hasard}\:\mathrm{8}\:{boules}\:{b}_{\mathrm{1}} ...{b}_{\mathrm{8}} \\ $$$${dans}\:\mathrm{6}\:{tiroirs}\:{t}_{\mathrm{1}} ...{t}_{\mathrm{6}} .{soit}\:{A}_{{i}} \:{l}'{evenement} \\ $$$$``{le}\:{tiroir}\:{t}_{{i}} \:{est}\:{vide}''\:{les}\:{evenements}\:{A}_{\mathrm{1}} {et} \\ $$$${A}_{\mathrm{2}} {sont}-{ils}\:{independants}\:? \\ $$

Question Number 149463    Answers: 1   Comments: 0

Let the independent random variables X_1 and X_2 have binomial distribution with parameters n_1 =3,p=2/3 and n_2 =4 p=1/2 respectively. Compute P(X_1 =X_2 )

$$\mathrm{Let}\:\mathrm{the}\:\mathrm{independent}\:\mathrm{random}\:\mathrm{variables} \\ $$$$\mathrm{X}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{X}_{\mathrm{2}} \:\mathrm{have}\:\mathrm{binomial}\:\mathrm{distribution} \\ $$$$\mathrm{with}\:\mathrm{parameters}\:\mathrm{n}_{\mathrm{1}} =\mathrm{3},\mathrm{p}=\mathrm{2}/\mathrm{3}\:\mathrm{and}\:\mathrm{n}_{\mathrm{2}} =\mathrm{4} \\ $$$$\mathrm{p}=\mathrm{1}/\mathrm{2}\:\:\mathrm{respectively}.\: \\ $$$$\mathrm{Compute}\:\mathrm{P}\left(\mathrm{X}_{\mathrm{1}} =\mathrm{X}_{\mathrm{2}} \right) \\ $$

Question Number 149406    Answers: 0   Comments: 0

if x has a binomial distribution with n=10 and p=(1/3).Find E(e^(3x) )

$${if}\:{x}\:{has}\:{a}\:{binomial}\:{distribution}\:{with}\:{n}=\mathrm{10}\:{and}\:{p}=\frac{\mathrm{1}}{\mathrm{3}}.{Find}\:{E}\left({e}^{\mathrm{3}{x}} \right) \\ $$

Question Number 149030    Answers: 0   Comments: 0

f(x)=4_−_(5^x +1) x=0,1,2..... find the moment generating function

$$\mathrm{f}\left(\mathrm{x}\right)=\underset{\underset{\mathrm{5}^{\mathrm{x}} +\mathrm{1}} {−}} {\mathrm{4}}\:\:\:\:\mathrm{x}=\mathrm{0},\mathrm{1},\mathrm{2}.....\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{moment}\: \\ $$$$\mathrm{generating}\:\mathrm{function} \\ $$

Question Number 149440    Answers: 1   Comments: 0

Question Number 148864    Answers: 1   Comments: 0

A random variable K has a pdf f(k)={_(0 , otherwise) ^e^(−k , 0>k) find E(K) and the cdf

$$\mathrm{A}\:\mathrm{random}\:\mathrm{variable}\:\mathrm{K}\:\mathrm{has}\:\mathrm{a}\:\mathrm{pdf}\: \\ $$$$\mathrm{f}\left(\mathrm{k}\right)=\left\{_{\mathrm{0}\:\:\:\:\:\:,\:\:\:\:\:\:\:\mathrm{otherwise}} ^{\mathrm{e}^{−\mathrm{k}\:\:\:,\:\:\:\:\:\:\:\:\mathrm{0}>\mathrm{k}} } \:\:\:\:\mathrm{find}\:\mathrm{E}\left(\mathrm{K}\right)\:\mathrm{and}\:\right. \\ $$$$\mathrm{the}\:\mathrm{cdf} \\ $$

Question Number 148620    Answers: 1   Comments: 0

consider the following pdf of a random variable X f(x)={Σ_(i=0) ^∞ [(−x^2 )i/i!]_(0 otherwise) ^(x>0) find the variance X

$$\mathrm{consider}\:\mathrm{the}\:\mathrm{following}\:\mathrm{pdf}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{random}\:\mathrm{variable}\:\mathrm{X} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\left\{\sum_{\mathrm{i}=\mathrm{0}} ^{\infty} \left[\left(−\mathrm{x}^{\mathrm{2}} \right)\mathrm{i}/\mathrm{i}!\right]_{\mathrm{0}\:\mathrm{otherwise}} ^{\mathrm{x}>\mathrm{0}} \:\right. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{variance}\:\mathrm{X} \\ $$$$ \\ $$

Question Number 148569    Answers: 2   Comments: 1

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