1-aN 1-a [1] It is well known that a finite geometric series for a # 1...

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1-aN 1-a [1] It is well known that a finite geometric series for a # 1 can be expressed Σ-1a³-¹ Consider a sample space, S, of outcomes wj, j = 1, 2, ..., N where p(w;+1) = 2 * p(w;) for all j, and let p₁ = p(w₁). Thus, with a = 2, p₁(1+2 +2²+...+ 2N-¹) = P(S). [a] What must the value of p₁ equal in order for the probability of the sample space to equal 1? [b] Write the probability of the event A = U₁=1 @j Note: both [a] and [b] need to be expressed concisely using the finite geometric series result. = 1-aN 1-a [1] It is well known that a finite geometric series for a # 1 can be expressed Σ-1a³-¹ Consider a sample space, S, of outcomes wj, j = 1, 2, ..., N where p(w;+1) = 2 * p(w;) for all j, and let p₁ = p(w₁). Thus, with a = 2, p₁(1+2 +2²+...+ 2N-¹) = P(S). [a] What must the value of p₁ equal in order for the probability of the sample space to equal 1? [b] Write the probability of the event A = U₁=1 @j Note: both [a] and [b] need to be expressed concisely using the finite geometric series result. =

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