Let Yn:nge1 be a sequence of independent and identically distributed random variables, where Y1simBernoulli(tfrac12). Define Z=sumn=1^infty4Yn/5^n. Then, which of the following statements is true?

(A) P(Zgetfrac35)=0.5, P(Z=tfrac425)=0

Q50Section B (Part B)50 of 120

Probability — a random series with Bernoulli digits

Let $\{Y_n:n\ge1\}$ be a sequence of independent and identically distributed random variables, where $Y_1\sim\text{Bernoulli}\left(\tfrac12\right)$ . Define $Z=\sum_{n=1}^{\infty}\dfrac{4Y_n}{5^n}$ . Then, which of the following statements is true?

Pick an option to check your answer.

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