(Frog) A frog lives in a garden where there are two ponds, see Figure 2. It spends 1/4 of its time in the large pond and the rest in the small pond. When it is in either of the ponds, we model its position as uniformly distributed. (a) What is the joint pdf of the vector that indicates the position of the frog in the diagram? (b) What is the marginal pdf of the horizontal position of the frog (i.e. its position on the horizontal axis)? Sketch the pdf. (c) If we know that the horizontal position of the frog is 3, what is the conditional pdf of its vertical position given this information? Sketch the pdf. ((1) Is the vertical position of the frog independent from the horizontal position of the frog? Justify your answer mathematically. (e) Is the vertical position of the frog conditionally independent from the horizontal position given the event the frog 3'3 in the small pond? Justify your answer mathe matically. Figure 2: The two ponds