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Solve the following problems using linearity of expectation. . (For each problem you will want to think about what the appropriate random variables should be and define them explicitly.)
(a) A coin with probability p of coming up heads is tossed independently n times. What is the expected number of maximal "runs", where a "run" is a maximal sequence of consecutive flips that are the same? For example, the sequence HHHTTHTHHH has 5 runs, the first three H, the following two T, and so on.
(b) A certain bubble gum company includes a picture card of a famous basketball player in each pack of bubble gum it sells. A complete set of cards consists of n players. Suppose that every pack you buy is equally likely to contain the picture of any of the n players. Let X be the random variable which is the number of packs you need to buy to have a complete set. What is E(X )? (Hint: think about representing X as the sum over i of the number of steps needed to go from having a set with i distinct players to i + 1 distinct players.)
One interesting application of computers is drawing of graphs and bar charts (sometimes called histograms). Write down script which reads five numbers between 1 and 30.
With mean call duration of six minutes. Ten percent of calls are long distance. Determine the maximum number of telephones an end office can support?
In your opinion, does framework necessarily lead to the top-down approach to development, e.g. you start with models in row 1, then work on row 2 models, and so on?
When you try to open the file in an image viewer, a message is displayed indicating that the file is corrupt. Write a 2-3 page report explaining how to recover the file, orkty.zip, for further investigation.
Write down the difference between system software and application software? Choose two of the application you listed and describe how you determine version of these programs. What specific features do you like about each program?
Create a cron file that will regularly perform the following back ups: performs a level 0 backup once per month and performs a level 2 dump one day per week
Recognize what you believe to be next set of core future service(s) to be offered via Internet over next 2 to 5 years based on current and evolving technologies.
Have you contacted State Historic Preservation Office (SHPO) to see if the project is in designated area of coastal zone which is significant to the study, understanding, or illustration of national, state.
Determine the average seek time? Determine the average rotational latency? Determine the transfer time for a sector? Determine the total average time to satisfy a request?
What networking and communications changes were introduced in the past decade (2000s), and what were their implications?
Suppose that 30 pictures are sent per second. (This digital source is roughly equivalent to broadcast TV standards that have been adopted.) Determine the source rate R (bps).
Write down the functions and steps involved in various window applications. What is mail merge? Enumerate the steps involved in mail merge.
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