Let X denote a number of failures of a particular machine wi

Let X denote a number of failures of a particular machine within a month. Its probability mass function is given by:

Show work please so i can learn how to do it, thankyou

Solution

A)WE HAVE TO FIND PROBABILITY OF LESS THAN 3 FAILURE

NOW ACCORDING TO THE PMF WE WILL TAKE IN TO ACCOUNT THE PROBABILITY OF X<3

WHICH INCLUDES X=0,1,2

AND THERE RESPECTIVE PROBABILITIES ARE 0.17,0.23,0.19

WE NOW ADD ALL THE THREE PROBABILITY AND WILL GET THE REQUIRED ANSWER

HENCE 0.69 IS THE PROBABILITY OF FAILURE LESS THAN 3

B)EXPECTATION = X*P(X)

NOW TOTAL EXPECTATION = 0*P(0)+1*P(1)+2*P(2)+3*P(3)+4*P(4)+5*P(5)

= 0*0.17 +1*0.23+2*0.19+3*0.13+4*0.08 +5*0.2==2.32