A First Course in Probability (10th Edition)

Chapter 6

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  ; There are white and red balls out of 13 ... more

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; There are white and red balls out of 13 balls... more

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; Let a random variable be the number of failure... more

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Yes. ; Since, the exponential function is non-... more

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0.265 ; Let and be the random variables, that ... more

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; Let the arrival timing of man and woman at a ... more

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, for . ; Let denotes the vehicle A location and... more

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; Since, three points are being randomly selected... more

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In the first case variables are  independent, but ... more

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; It is given that is the number of people ... more

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The distribution of   ; Calculating That is,... more

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27.07 ; Calculating the value of Now defining a ... more

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There are three 1ndependent variables .The ... more

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The conditional mass function of given that ... more

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; Conditional density function of y given x is ... more

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The conditional density is and the expectation is... more

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0.5 ; We have to compute  ; By the symmetry , ... more

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; Distribution function for x is given as  ; T be... more

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; X1 , X2 , X3 denotes the point where trucks ... more

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0.7930 ; sample size is 5  that is Xi follow ... more

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; According to the question for , Because be the... more

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It is given that and are 2 independent standard ... more

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; Distribution function is obtained . The range ... more

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; Let and .It is asked to calculated the joint ... more

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; Using the transformation theorem, obtain the ... more

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Given .Then the p,d,f of can be calculated in the... more

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, \),   ;   ; (a) Jacobian Transformation:  ; (b... more

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; The joint probability density function of and... more

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; Let and be independent exponential variables ... more

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Thus, the joint mass function is symmetric, which ... more

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Since this is a symmetrical function of (xi,x2... more

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  ; Consider X and Y have a joint distribution ... more

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L and D should be known to calculate .  ; ... more

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; Consider the following figure:When L > D Needle... more

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; From the information, observe that X and Y are ... more

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Therefore, ; From the information, observe that  ... more

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Then the distribution of time that the flashlight ... more

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Since,, than Hence, proved ; To prove for to be ... more

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Therefore, given  the conditional density is still... more

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Hence,Probability =\)Probabilty for n-k failures... more

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The case is similar to the case of selection of  ... more

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; Let  are Poisson variates with means  ... more

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Therefore the required probability is: ; Let X and... more

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Hence, by joint distribution factors, there is an ... more

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Therefore, it can see that this is a form of Gamma... more

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Probability of A saddle point in a array of size n... more

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Hence, by joint distribution factors, there is an ... more

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If . Then at least two persons will be at a ... more

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; Differentiating both sides with respect to ... more

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Thus if observe find that (1) is a Beta function ... more

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; The order statistics of a random sample are the... more

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; The following steps can be used to find the ... more

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; Let be the order values of n independent ... more

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It is given that Thus,Now calculating .Now making ... more

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; Let  be independent uniform (0, 1) random ... more

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 This is a Cauchy distribution. ; It is given that... more

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The probability of beta distribution is given by ... more

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; The distribution of Dirichlet is a family of ... more

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Let be random variable such that and are ... more

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1 ; 1 ; \[J(x_1,...,x_n)=\begin{vmatrix}\frac{\... more

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Let be multinomial random variable that denote ... more

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; Let define random variables and to denote the... more

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is not independent of XN. ; X1,X2,... be a ... more

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is not independent of XN. ; X1,X2,... be a ... more

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The bid of three other persons follows uniform ... more

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Probability of given is given by Hence from the ... more

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; Assume , , if there have been failure after ... more

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; Assume be a Pareto random variable with ... more

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Condition distribution function of and   is given... more

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