Conditional Probability in Geometric DistributionMs. A is taking driving test to get her driving license. The probability of passing a test is 0.3 which remains same no matter how many times she takes the test. Let X is a random variable which is the number of tests she takes to get her license.1) Use conditional probability rule to determine her chance of getting the license on the 6th test starting from her first attempt considering it is known that she has already failed on the first 4 tests.2) Though one can take the driving test 6 times within a six-month period, he/she can take tests until getting licensed. How many tests is Ms. A expected to take to get the license? What is the standard deviation of the number of tests she takes to get licensed?

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losnonamern · Accepted Answer

Step 1You need to use the geometric distribution properties:      E    (  X  )  =            1      p        =      1    0.3    =      10    3          V    a    r    (  X  )  =                    1        −        p                    p        2              =            1      −      0.3              0.3      2        =      70    9  Step 2And combine these with memorylessness to obtain:       E    (  X  ∣  X  ≥  4  )  ,      V    a    r    (  X  ∣  X  ≥  4  )Hint:       E    (  X  +  a  )  =      E    (  X  )  +  a  ,      V    a    r    (  X  +  a  )  =      V    a    r    (  X  )

Ms. A is taking driving test to get her driving license. The probability of passing a test is 0.3 which remains same no matter how many times she takes the test. Let X is a random variable which is the number of tests she takes to get her license.

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