Question

1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH, have a waiting time during peak rush hour periods of eight minutes ("2012 annual report," 2012). (a) State the random variable.(b) Find the height of this uniform distribution.

Answer 1

Answer:

a) For this case we define the random variable as X ="waiting time during peak hours" and we know that this distribution follows an uniform distribution:

$X \sim Unif(a=0,b=8)$

Where a and b represent the limits of the distribution.

b) $f(x) = \frac{1}{8}= 0.125, a\leq x \leq b$

And the height for this case would be 0.125

Step-by-step explanation:

Part a

For this case we define the random variable as X ="waiting time during peak hours" and we know that this distribution follows an uniform distribution:

$X \sim Unif(a=0,b=8)$

Where a and b represent the limits of the distribution.

Part b

For this case the density function would be given by:

$f(x) = \frac{1}{8}= 0.125, a\leq x \leq b$

And the height for this case would be 0.125

And $f(x)= 0$  for other case.

The cumulative distribution function would be given by:

$F(x) = 0, x<0$

$F(x) = \frac{x-a}{b-a}= \frac{x}{8}, 0\leq x < 8$

$F(x) = 1, x\geq 8$