1 . A bag contains { coins , ? of which have a head on both sides while the other 1 coins* are normal . A coin is chosen at random from the bag and

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1 . A bag contains { coins , ? of which have a head on both sides while the other 1 coins*are normal . A coin is chosen at random from the bag and tossed ?' times . The numberof heads obtained is a random variable , say`( a ) What are the possible values of ^! Also tabulate the point of*`(^` Calculate FIX'; and Vall*^2. A moment - generating function of * is given by Miley = 1.30 + 0. 10"' + 0. 2,* + 0. 10^( A) Find the point of*`( h ) Find the values of " and ` for*`( c ) Calculate Pl* = 2)( ^ ) Calculate [ 12`] .$. Police are to conduct random breath testing on drivers on a busy mad one Fridaymining . Suppose`` of the drivers drink and drive at the time . Let* be the numberof drivers that police need to test to get the first case of drinking and driving . Let }"he the number of drivers tested to get & such cast`( a ) Name the probability" distribution and specify the wake of any parameter ( s ) forLack of the two random variables{ and }" .`I'm` What is the probability that at least .* drivers are to he tested to get the first*drinking and driving case!"( c ) What is the probability that exactly all drivers are to be tested to get` drinking*and driving cases?"I'll On average , how many drivers do police head to test to get & cases of shrinkingAnd thriving"( e ) Find Fly _ SOY .I'll Suppose the police have not found any case of drinking and driving in their first*$ tests . What is the conditional probability that the police still cannot find any*case in their next & tests!"IF] What is the probability that the police will find exactly' I cases of drinking and!driving in testing 200 driver ?" At least two different probability distributions call`he used to calculate / approximate this probability . Which two , and how differentare the results'?"