A First Course in Probability (10th Edition)

Chapter 4

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; Assume, be the winnings, it can be positive or... more

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1234568910121516182024253036 ; Assume be the ... more

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3456789101112131415161718 ; Assume be the sum of ... more

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12345678910 ; Assume be the random variable ... more

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where . ; Assume represents the difference ... more

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13 ; Assume represents the difference between the... more

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(a).123456 (b).123456 (c).23456789101112 (d).-5-4-... more

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where, ; Assume, be the random variable ... more

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 Let be an event in which the gambler won a ... more

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0500100015002000 ; Assume, be the random variable... more

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01234 ; Assume, be the random variable ... more

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12340.16670.15560.14350.5342 ; Assume, be the ... more

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; denote the number of correct guesses yield  by... more

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Therefore, So,     therefore the plot of the ... more

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; Since from the given expression for see that... more

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A company should charge (0.1+p)A ; The expected ... more

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3/5 or 0.6 ; Let X be the number of defective ... more

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; If we check in order (1,2),then, the expected ... more

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; Let the expected score and the probability  ... more

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7.51 ; Let X be the random variable.That is, X= ... more

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10/3 ; Binomial distribution Expected value = np... more

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+1  items will lead to maximum expected profit. ; ... more

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; Let the two possible values of be 2 and 3. ... more

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82.5536 and 84.5 ;   ; more

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3/8 ; Three black and three white balls are found ... more

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; Let X be the random variable.X=The number of ... more

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0.171875 ; Let x be the random variable and the ... more

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0.05792 ; The value for i=3 is  ; Here the ... more

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; And the combination is given by ; Let the ... more

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5 examiners have high chances to pass and it is ... more

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;    ; Probability that a guilt is proved ... more

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; The probability of begin defective is given by ... more

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; Initially find for female and maleProbability ... more

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0.03 ; x marks the number of errors   ; more

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253 ; total people : n  ;   = ; required ... more

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It is very likely that the drug is beneficial for ... more

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0.408 ; use poisson model ; probability to get at ... more

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\[exp(-n(n-1)/2\cdot \sum_{1}^{k}pj^{2}\] ; use ... more

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; It is stated that there are couplesHere couple... more

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; From the provided data it is observed that in ... more

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; & ; It is stated that ,at time 0 a coin is ... more

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probability that stronger team wins in exactly i=4... more

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7 ; probability of each team winning ; 1/2 ; one ... more

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has negative binomial distribution. ; The ... more

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f(n)=1+log2n ; assumptions ; you can see in power ... more

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; factor 2 is because the considered box is not ... more

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; probability of choosing 2 white and 2 black ... more

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100% and 25% respectively for i=1,4  ; for i=1 ... more

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0.3439 ; Required probability x is number of ... more

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1.5 ; Let total number of accidents be N. ; more

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The expected number of distinct types that appear ... more

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; Consider , that is denotes have not picked a ... more

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The distribution of can be written as composition ... more

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The distribution of can be written as composition ... more

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The given conditions are proved for non negative ... more

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Based on that two possible values can be proved ... more

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; Define random variable , and expectation of is... more

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; is a random variable and assume , are two ... more

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proved that the sum of all possible probabilities ... more

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with parameter and . ; Expectation of the function... more

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Thus, Therefore,Now, and both are less than as... more

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  ; That the probability for successes in trails... more

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; Let be the number of nonfunctional components ... more

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 The above expression when equal to zero for to ... more

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Hence it is shown that probability that an even ... more

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For this fraction is greater than or equal to one... more

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; We have ; Since log is a strictly increasing ... more

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  ; We know that Now use and So we have answer... more

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It is wrong because it is not mentioned that in ... more

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 Hence proved. ; To prove that,Therefore, ... more

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Use the definition of conditional probability and ... more

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Hence proved. ; To prove that events and are ... more

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; The probability of a hypergeometric random ... more

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; If chips out of exceed all the numbers left ... more

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The probability mass function of is, ; From the ... more

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A jar contains  chips. A boy successively draws ... more

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Hence proved   For large ; The is, ; Similarly, ... more

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1.075 ; Let us suppose that random variable is ... more

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; Observe that the value of is fully determined ... more

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; It is clear that the coin was flipped comes up ... more

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; Probability that a randomly chosen family will ... more

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;  From the question it is clearly show that, If ... more

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The required expected payoff is .So, if the ... more

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; It can be noted that the number of successes ... more

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0.2001 ; Expected value is .Variance .Where is ... more

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; Let  denote the number on the ball drawn, =1,... more

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0.4154 ; If it wins the weekend Game, Then ; and... more

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0.7000 ; Consider this as the binomial experiment ... more

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0.2301 ; Let the number of events is represented ... more

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; By using poisson distribution conditions,Now ... more

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; Here, is denote the  parameter , and Let (q=1-... more

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; A total number of white balls will be drawn ... more

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Binomial random variable with parameter and . ; ... more

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