Final answer:
The probability that the value of the stock is more than $19 is 7/13 or approximately 0.5385.
Step-by-step explanation:
To find the probability that the value of the stock is more than $19, we need to calculate the area under the probability density function (PDF) curve for values greater than $19. Since the stock value follows a uniform distribution, the PDF is constant within the range $13 to $26. The total area under the PDF curve is equal to 1.
The width of the uniform distribution is given by the difference between the maximum value ($26) and the minimum value ($13), which is $26 - $13 = $13. Therefore, the height of the PDF curve is equal to 1/$13 = 1/13.
To find the probability that the value of the stock is more than $19, we need to calculate the area of the rectangle bounded by $19 and $26 and divide it by the total area under the PDF curve. The area of the rectangle is equal to the width ($7) multiplied by the height (1/13), which is $7/13. Therefore, the probability that the value of the stock is more than $19 is 7/13 or approximately 0.5385.