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Answer:
The expected cost is 152
Step-by-step explanation:
Recall that since Y is uniformly distributed over the interval [1,5] we have the following probability density function for Y
if
and 0 othewise. (To check this is the pdf, check the definition of an uniform random variable)
Recall that, by definition
Also, we are given that . Recall the following properties of the expected value. If X,Y are random variables, then
Then, using this property we have that .
Thus, we must calculate E[Y] and E[Y^2].
Using the definition, we get that
Then