1. [7 marks] Consider the following probability density function for the continuous random variable X: *Note: The height of the larger triangle is 4/3 2/3 and the height of the second is 2/3. Also, both triangles are symmetric about their peaks. f( x) X (a) Verify that the distribution defined above satisfies the conditions of a continuous probability model. Recall that the geometric area of a triangle is A = ,bh, where b = the length of the base of the triangle, and h = the height of the triangle. (b) Determine the following probabilities. Leave all answers in exact form (i.e., no decimals). (i) P(X