A needle is tossed at random on a grid of equally spaced, Basic Statistics

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A needle is tossed at random on a grid of equally spaced

Question: A needle is tossed at random on a grid of equally spaced parallel lines. Assume the needle is so much longer than the spacing between the lines that the possibility of the needle not crossing any line can be neglected. Let X be the distance between the center of the needle and the closest point at which the needle crosses one of the lines. Find:

a) The distribution function of X:

b) The density function of X.

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Basic Statistics: A needle is tossed at random on a grid of equally spaced

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