Identically distributed random variables

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Let X, X1, X2, ... be independent, identically distributed random variables, such that P(X = 0) = P(X = 1) = 1/2.

(a) Let N1 be the number of 0's and 1's until the first appearance of the pattern 10. Find E N1.

(b) Let N2 be the number of 0's and 1's until the first appearance of the pattern 11. Find E N2.

(c) Let N3 be the number of 0's and 1's until the first appearance of the pattern 100. Find E N3.

(d) Let N4 be the number of 0's and 1's until the first appearance of the pattern 101. Find E N4.

(e) Let N5 be the number of 0's and 1's until the first appearance of the pattern 111. Find E N5.

(f) Solve the same problem if X ∈ Be(p), for 0<p<1.

Reference no: EM131830173

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