Question

1. A device that continuously measures and records seismic activity is placed in a remote region. The time T, failure of the device is exponentially distributed with mean 3 years Since the device will not be monitored during its first two years of service, the time to discovery of its failure is X max(T, 2). Then E(X) - 2. The loss due to fire in a commercial building is modelled by a random variable X with probability density function f(x)-(0.00020-x) otherwise 20 for 0 <x<20 Given that a fire loss exceeds 8, the probability that it exceeds 16 is Suppose that the moment generating function Mx (t) of the continuous random variable X has the property Mx (t)-e Mx(t) for all t. Then the mean of X is 3. 4. An undergraduate student has asked a professor for a letter of recommendation. He estimates that the probability he will get the job is 0.8 with a strong letter, 0.4 with a medium letter and 0.1 with a weak letter. He also believes that the probabilities that the letter will be given strong, medium or weak are 0.5, 0.3 or 0.2 respectively. The probability that the letter was strong given that he got the job is

Answer 1

1. sol:

max(T, 2) 느 we (arn 2 ,TZ2 E(x) - 2

tis 2 3 2 e773 4.5670 Elx) 4.567

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