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Answer:
a) 0.31 = 31%
b) 0.03 = 3%
c) 0.36 = 36%
d) 2 times
Step-by-step explanation:
If is the cumulative distribution function of the random variable X, then by definition the probability P of the random variable is given by
If additionally the random variable is discrete (only has non-negative integers as outcomes as is the case in this problem) then
a)
We are looking for P(X<2)
b)
In this case we want P(X>3)
c)
Now, we are interested in P(X=1)
d)
The expected number of times that the process is recalibrated during the week is the expected value of the probability distribution:
P(X=1)+2P(X=2)+...+nP(X=n)+...
But it is easy to see that P(X=n) = 0 if n is an integer >4
So, the expected value is
P(X=1)+2P(X=2)+3P(X=3)+4P(X=4)
We already have P(X=1) and P(X=2). Let's compute the rest
and the expected value is
0.36 + 2*0.53+3*0.13+4*0.03= 1.93 = 2 times rounding to the nearest integer.