Suppose X is uniformly distributed over the interval .Find P(3

Question

Suppose X is uniformly distributed over the interval  .Find P(3 < X < 8).

Quizplus · Accepted Answer

The interval 11ea83f6_6397_afcc_b5a5_615dc1a70ddd_TB6578_11_TB6578_11 is equivalent to the interval [0,1] (this is the interval that random numbers generated by a computer program typically fall into). Since X is uniformly distributed over this interval, the probability of any sub-interval is simply the length of that interval. Therefore, the probability of 3 < X < 8 is the same as the length of the interval (8-3) divided by the length of the whole interval (1-0), which is 5. Thus, P(3 < X < 8) = 5/11ea83f6_6397_afcc_b5a5_615dc1a70ddd_TB6578_11_TB6578_11. This is equivalent to the hexadecimal value 11ea83f6_6397_d6df_b5a5_c5445ddc6037_TB6578_11_TB6578_11, which corresponds to choice C.

Suppose X Is Uniformly Distributed Over the Interval