X is a random variable which represents the number of hours

X is a random variable which represents the number of hours required to replace a failed compressor. The probability mass function (PMF) for x is given by:

a. Find the probability that replacement of the compressor will take exactly 3 hours.

b. Find the probability that replacement of the compressor will take more than 3 hours.

c. What is the mean or expected number of hours to replace the compressor?

X is a random variable which represents the number of hours required to replace a failed compressor. The probability mass function (PMF) for x is given by: a. Find the probability that replacement of the compressor will take exactly 3 hours. b. Find the probability that replacement of the compressor will take more than 3 hours. c. What is the mean or expected number of hours to replace the compressor?

Solution

(a) P(X=3) =(1/2.45)/3=0.1360544

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(b)P(X>3) = P(X=4)+P(X=5)+P(X=6)

=(1/2.45)/4 + (1/2.45)/5+ (1/2.45)/6

=0.2517007

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(c) mean= sum of x*f(x)

=1*(1/2.45)/1+ 2*(1/2.45)/2+3*(1/2.45)/3+4*(1/2.45)/4+5*(1/2.45)/5 +6*(1/2.45)/6

=2.44898