Suppose I’m placing 6 volumes of a mathematics book series on my shelf, but I’m in ahurry and my office is a mess, so I just put them on the shelf randomly. Assume that allpossible orderings of the 6 volumes are equally likely to occur. Also, note that each volumeis numbered “Volume 1”, “Volume 2”, etc.Let X = the number of volumes that are in the correct spots before the first incorrectlyplaced volume. For example: X = 3 for the arrangement 1, 2, 3, 5, 4, 6, since the first3 volumes are placed correctly, then the 4th spot has Volume 5 in it. Another example:X = 0 for 2, 6, 3, 4, 5, 1, since the very first spot has the wrong volume in it!(a) Find the support for X.(b) Compute the probabilities that X = x for each value x in the support in X.(c) Use the probabilities to determine the formula for the PMF as a singlefunction pX (x) = P (X = x) with input x
Suppose I’m placing 6 volumes of a mathematics book series on my shelf, but I’m in a
hurry and my office is a mess, so I just put them on the shelf randomly. Assume that all
possible orderings of the 6 volumes are equally likely to occur. Also, note that each volume
is numbered “Volume 1”, “Volume 2”, etc.
Let X = the number of volumes that are in the correct spots before the first incorrectly
placed volume. For example: X = 3 for the arrangement 1, 2, 3, 5, 4, 6, since the first
3 volumes are placed correctly, then the 4th spot has Volume 5 in it. Another example:
X = 0 for 2, 6, 3, 4, 5, 1, since the very first spot has the wrong volume in it!
(a) Find the support for X.
(b) Compute the
(c) Use the probabilities to determine the formula for the PMF as a single
function pX (x) = P (X = x) with input x
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