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tigry1 [53]
3 years ago
7

1.) The commuter trains on the Red Line for the Regional Transit Authority (RTA) in Cleveland, OH, have a waiting time during pe

ak rush hour periods of eight minutes ("2012 annual report," 2012). (a) State the random variable.(b) Find the height of this uniform distribution.
Mathematics
1 answer:
alisha [4.7K]3 years ago
3 0

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

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

F(x) = 1, x\geq 8

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