Question

In a typical movie with a haunted house, a character goes off to investigate something alone, on average, every 17.2 minutes. (a) What is the probability that the first time that a character investigates something alone will happen more than 15 minutes after the beginning of the movie? (b) If no character has investigated anything alone by 26 minutes into the movie, what is the probability that the first occurrence will take place at least 41 minutes into the movie?

Answer 1

a)

here for exponential distribution paramter $\beta$ =17.2

hence P(first time a harecter investigation is more than 15 minutes after)=P(X>15)=e^{-x/ $\beta$}

=e^-15/17.2=0.4181

b)

P(X<41|X>26)=P(26<X<41)/P(X>26)=((1-e^-41/17.2)-(1-e^-26/17.2))/(e^-26/17.2)=0.5819