For each of the following cases write down an expression for and sketch the distribution function...

 

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For each of the following cases write down an expression for and sketch the distribution function of the random variable Z: (a) A coin is tossed repeatedly until a head is obtained for the first time. Z is the number of tosses required. (b) A point in the zy- plane is chosen at random from the interior of a circle for which the equation is ² + y² = 1 and the probability that the point will belong to any region inside the circle is proportional to th area of that region. Z is the distance from the center of the circle to the point. (c) Suppose that X has a uniform distribution on the interval (0,5) and the random variable Z=0 if X ≤ 1, 2=5 if X2 3 and Z = X otherwise. For each of the following cases write down an expression for and sketch the distribution function of the random variable Z: (a) A coin is tossed repeatedly until a head is obtained for the first time. Z is the number of tosses required. (b) A point in the zy- plane is chosen at random from the interior of a circle for which the equation is ² + y² = 1 and the probability that the point will belong to any region inside the circle is proportional to th area of that region. Z is the distance from the center of the circle to the point. (c) Suppose that X has a uniform distribution on the interval (0,5) and the random variable Z=0 if X ≤ 1, 2=5 if X2 3 and Z = X otherwise.

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it z random Variable representing the distance between the middle o... View the full answer