# Thread: Discrete Random Variable

1. ## Discrete Random Variable

Let x be a geometrically distributed random variable having parameter p. Let Y = X if X < M and let Y = M if X >= M; that is, Y = Min(X, M). Compute the density of Y.

So the density of Y will be split into two cases
Case 1: For values from 0 to M-1, which will just be the geometric density.
Case 2: For the value M.

How do you calculate the density when the value is equal to M?
(Is there a way to find it without using the definitions of a density function by doing 1 - (all the values in case 1))

Thanks

2. Originally Posted by feiyingx Let x be a geometrically distributed random variable having parameter p. Let Y = X if X < M and let Y = M if X >= M; that is, Y = Min(X, M). Compute the density of Y.

So the density of Y will be split into two cases
Case 1: For values from 0 to M-1, which will just be the geometric density.
Case 2: For the value M.

How do you calculate the density when the value is equal to M?
(Is there a way to find it without using the definitions of a density function by doing 1 - (all the values in case 1))

Thanks
p(y=M) = p(x>=M)

RonL

3. Thanks =P

Is there way to find the survival function of a geometric RV without doing 1-F(X)?

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