5. A probability density function is a function, f (x ), for which the probability that another quantity, ), is between a and b is equal to [ f (x) dx . In statistics, X is called a continuous random variable, and the notation P(as X sb) is used for "the probability that \\" is between the values a and b." So, P(asxsb ) = [ f (x) Consider the probability density function f (x) = , defined for all real numbers. A typical ( x - xo ) + 72 graph of this function is below: 1-1 1.2 1.3 1.4 1.5 16 1.8 The parameters x, and y affect the horizontal position and width of the "peak" of the graph, respectively. Note that this graph extends left and right forever, indicating a clustering of \\ near X, . (A) In the graph above, use the definitions and notation to write what the shaded region represents, as a definite integral equal to a probability in terms of x, and y . (4pts) (B) Determine the general antiderivative of f with respect to x, assuming x, and y constant. Remember: show every step! (Hint: factor y from the denominator) (9pts)(C) Suppose x, =1.4 and y = 0.05 . Determine the probability that \\" is between 1.35 and 1.45. (3pts) (D) Suppose x, =1.4 and y = 0.05 . Determine the probability that \\" is between 1.25 and 1.5. (3pts) (E) Suppose x, =1.4 and y =0.05. Use technology to sketch a graph of y = f(x) , and shade the region which represents the probability from part D. (2pts)