How the poisson probability distribution function

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Reference no: EM132797308

Question 1:

A satellite receives messages at random and at an average rate of 1.4 per microsecond.

(a) Describe how the Poisson probability distribution function may be applied to this problem to determine the probability of a given number of messages arriving in a set interval.

(b) Find the probability of 7 messages arriving in a 3 microsecond interval.

(c) For how long can the reception of messages be interrupted, if the probability of missing one or more messages is to be no more than 0.05.

Question 2:

A model for the time to failure in years, T, of an engineering component has the probability density function:
f (t) = kt² (5 - t) 0<t<5
= 0 otherwise

Thus, given that:

₀∫^∞ f (t) dt = 1

(a) Show that k = 12/625

(b) Find the mean time to failure.

(d) Find the probability that the device fails between 0 and 3 years. Hence show that the median lifetime is greater than 3.

Attachment:- sample.zip

Reference no: EM132797308

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