Show all woprk

6. (9 pts) The probability density curve of a random variable X is given in the following figure. The possible values for X range from 20 to 50. 20 30 a) Find the height of the density curve between 20 and 50. (3) b) Find the probability that X is between 25 and 40. (3) c) Is the random variable X discrete or continuous? Why? Select the correct explanation. (3 pts) 1 . The random variable X is discrete, because the sample space [20,50] is finite. ii. The random variable X is continuous because there is an infinite number of possible values in the interval [20,50]. iii. The random variable X is discrete because the length of the interval [20,50] is finite. iv . The random variable X is continuous because the length of the interval [20,50] is finite