Question: 1. Consider the following random experiment : we toes a fair coin repeatedly until the first heads occurs. The outcome @ is the number of

1. Consider the following random experiment : we toes a fair coin repeatedly until the first "heads" occurs. The outcome @ is the number of coin flips in this sequence before (i.e. not including ) the first heads . (a) Describe the probability space corresponding to this random experiment , detailing each component. Make sure to define what probability is assigned to any set in the -algebra . (b) Consider the random variable X (w ) returning the value l ifw 0. (a) Compute P(X > 0.5) for a = 1 and b = 0.5. (b) Find the support of X . Is X discrete, continuous, or neither (mixed)? Justify. (c) Derive the probability density function (pdf ) of X. (d) Consider the transformation Y = g(X ) = 1/X . Find the pdf of Y

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