A subway train on the #6 line arrives every two minutes. We are interested in th

Question

A subway train on the #6 line arrives every two minutes. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution. In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest 0.01. a. The waiting time is modeled by a random variable X with x ~ (pick one) distribution b. The density function for X is given by f(x) = with lessthanorequalto X lessthanorequalto C. The mean mu_x = d. The standard deviation sigma_x = e. The probability that the commuter waits less than one minute is

Explanation / Answer

a) uniform distribution ; U(0,2)

b) fx =1/(b-a)=1/2 =0.5 with 0<=X<=2

c)mean =(a+b)/2 =(0+2)/2=1

d)standard deviation =(b-a)/(12)1/2 =0.5774

e)probability =P(X<=1)=(1-0)/(2-0)=1/2=0.5

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