(ii) A 2⁶ factorial experiment is conducted in blocks of size 2³. Write the confounded effects such that no main effect or two factor interaction are confounded. Give the list of independent and generalised interactions confounded along with the elements of key block only.

(iii) Give the break-up of degrees of freedom for a 2ⁿ factorial experiment in 2ᵏ blocks.

3Medium15 marks

Let Yᵢ, i ≥ 1 be independent and identical U(-1, 1) random variables. Determine if the following sequences converge in probability :

(i) (Yᵢ / i)

(ii) (Yᵢ²)

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