Let H k (n) be the number of vectors x 1 , , x k for which each x i is a positive integer satisfying 1 x i n and x 1 x 2 x k (a) Without any computations, argue that H 1 (n) n How many vectors are there in which x k j (b) Use the preceding recursion to compute H 3 (5) First compute H 2 (n) for n 1,...

a The number of vectors that have x k j is equal to the number of vectors x 1 ...

Let H k (n) be the number of vectors x 1 , . . ., x k

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Let H_k(n) be the number of vectors x₁, . . ., x_k for which each x_i is a positive integer satisfying 1 ≤ x_i ≤ n and x₁ ≤ x₂ ≤ . . . ≤ x_k.

(a) Without any computations, argue that H₁(n) = n

How many vectors are there in which x_k = j?

(b) Use the preceding recursion to compute H₃(5).

First compute H₂(n) for n = 1, 2, 3, 4, 5.

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A First Course In Probability

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9th Edition

Authors: Sheldon Ross

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Let H k (n) be the number of vectors x 1 , . . ., x k

Question:

Hа (n) 3D Н-10) k> 1 =1

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a The number of vectors that have x k j is equal to the number of vectors x 1 ...View the full answer

A First Course In Probability

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