The Department of Transportation (DOT) monitors sealed bids for new road construction. For new access roads in a certain state, let low bid (thousands of dollars) and let estimate of fair cost of building the road (thousands of dollars). The joint probability density of X and Y is f(x, y)= e^-y/10/10y 0< y

Complete Question

The complete question is shown on the first and second uploaded image

The  marginal density function of Y is  

The distribution is exponential distribution

and the expected value is

Step-by-step explanation:

From the question we are told that the function is  

Now the marginal density function of Y i.e f(y) is mathematically evaluated by obtaining the probability density function of y as follows

The distribution of the function above is exponential distribution with a rate parameter equals to  

  The mean DOT estimate E{Y} is mathematically evaluated as

    substituting value

where is the figure

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (