X ~ U(0,1) Find the 1st quartile or 25th & the 3rd quartile 75th percentile and the...

X ~ U(0,1)
Find the 1st quartile or 25th & the 3rd quartile 75th percentile and the median.

Help me please

Expert Solution

X is uniformly distributed in the interval (0,1).

The pdf (probability density function) of X is

The cdf (cumulative distribution function) of X is

The first Quartile, Q1, is the value of X, such that 25% of the values are below X=Q1. In other words, the probability that X is less than or equal Q1 is 0.25

The Third Quartile, Q3, is the value of X, such that 75% of the values are below X=Q3. In other words, the probability that X is less than or equal Q3 is 0.75

The Median, M, is the value of X, such that 50% of the values are below X=M (and 50% are above X=M). In other words, the probability that X is less than or equal M is 0.50

ans:

The 1st Quartile of X is 0.25
the 3rd Quartile of X is 0.75
The median of X is 0.50

orchestra answered 2 years ago

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