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Question 2 (25 points, Swimming Frog): A frog is dropped to a river with a width 10 meter. The location of the river where the frog lands on is random and can be considered uniformly distributed. After it gets dropped, the frog swims to the river-bank closer to it (See Fig. 1)· Let random variable X denote the distance that the frog swims to get back to the river-bank 10 m Figure 1: Diagram for Q2. Frog swims to the closest side (a) (10 Pts.) Determine the distribution of X. Justify your reasoning (b) (5 Pts.) From the distribution of X, determine P(X > 1) (c) (5 Pts.) Determine ELX (d) (5 Pts.) Determine the CDF of X, and then calculate P(X <5).

ANSWER

巳 «Ils on A 十一 l o U EX- 5

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