Question

A certain math instructor always arrives for class at most 5 minutes early or at most 5 minutes late Any amount of time early or late within the interval [-5,5] s eally likely, with negative values corresponding to being early and positive values corresponding to being late. a. What pdf would you choose to model the random variable X representing the amount of time early or late? b. Find the probability of being: ii. at most 2 minutes early; iv. neither more than 1 minute early nor more than 1 minute late. i. at least 3 minutes late; iii. exactly on time;

Answer 1

a) Uniform distribution

with a = -5 and b = 5

b)

P(X < x )= (x-a)/(b-a) = (x +5)/10

i) P(X < -3 )   = 2/10

ii) P(X < 2) = 7/10

iii) P(X = 0) = 0

iv) P(-1 < X < 1) = 2/10

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