Take a coin with P(H) = 1/n and toss it until you see (n +1) many H's for the first time. Let Xn be the number of times we observe two successive H's. For example, suppose n = 5, you wait for the sixth H, and the sequence of tosses are HHHTTHTTHH, then Xn = 3 because there are 3 times that we observe two successive H's. Required:a. Find lim P(Xn >= 2). n→ [infinity] b. Now suppose P(H) = 1/n^2 and, as before, toss it until you see (n +1) H's for the first time. Let Xn be the same as before. Find the exact expression of P(Xn = 0) and compute lim P(Xn = 0). n→ [infinity]

Savannah is painting a striped background for a mural on a wall that is 1515 yards long. she wants a total of 9696 stripes that are all the same width. which calculation should savannah use to decide how wide to make each stripe?

Aquality characteristic of new iphone x made at the amsterdam plant at apple computers has a manufacturing specification (in mm) of 0.200 +/- .07. historical data indicates that if the quality characteristic takes on values greater than 0.27 or smaller than 0.13 the component fails at a cost of20.19. based on these data: determine the taguchi loss function (must show work) calculate an estimated loss for a quality characteristic of .30 calculate an estimated loss for quality characteristic of .40.

Use a calculator to verify that σ(x) = 62, σ(x2) = 1034, σ(y) = 644, σ(y2) = 93,438, and σ(x y) = 9,622. compute r. (enter a number. round your answer to three decimal places.) as x increases from 3 to 22 months, does the value of r imply that y should tend to increase or decrease? explain your answer. given our value of r, y should tend to increase as x increases. given our value of r, we can not draw any conclusions for the behavior of y as x increases. given our value of r, y should tend to remain constant as x increases. given our value of r, y should tend to decrease as x increases.