Problem #3 PDF of continuous random variables. Suppose Cost is a continuous random variable whose possible...

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Problem #3 PDF of continuous random variables. Suppose Cost is a continuous random variable whose possible values are given by the interval 20 x 70, where x is in dollars million ($M). (1). Please find the value of constant c such that the function below is a PDF. Once you found the value of c, you are also required to present the complete PDF in the mathematical function format. (Hint: Now that you have learned about the triangular distribution, you can directly leverage its unique characteristics to save calculation time. However, you are still encouraged to double-check against the standard procedure through step-by-step calculation.) (4 points) fCost(x) 20 30 ($M) x 70 (2). Please determine the probability of the following events: P(Cost 30), P(30 Cost < 70), P(Cost = 30). (3 points) Problem #3 PDF of continuous random variables. Suppose Cost is a continuous random variable whose possible values are given by the interval 20 x 70, where x is in dollars million ($M). (1). Please find the value of constant c such that the function below is a PDF. Once you found the value of c, you are also required to present the complete PDF in the mathematical function format. (Hint: Now that you have learned about the triangular distribution, you can directly leverage its unique characteristics to save calculation time. However, you are still encouraged to double-check against the standard procedure through step-by-step calculation.) (4 points) fCost(x) 20 30 ($M) x 70 (2). Please determine the probability of the following events: P(Cost 30), P(30 Cost < 70), P(Cost = 30). (3 points)