A share of common stock in the Pilsdorff beer company has a price [math]Y_n[/math] on the [math]n[/math]th business day of the year. Finn observes that the price change [math]X_n = Y_{n + 1} - Y_n[/math] appears to be a random variable with mean [math]\mu = 0[/math] and variance [math]\sigma^2 =1/4[/math]. If [math]Y_1 = 30[/math], find a lower bound for the following probabilities, under the assumption that the [math]X_n[/math]'s are mutually independent.

• [math]P(25 \leq Y_2 \leq 35)[/math].
• [math]P(25 \leq Y_{11} \leq 35)[/math].
• [math]P(25 \leq Y_{101} \leq 35)[/math].