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Essay on Probability Theory and Random Variable

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Event A is rolling a die and getting a 6. Suggest another event (Event B) that would be independent from Event A.
A company runs 3 servers, each providing services to 40 computers. For each server, two of its client computers are infected. What is the probability that 3 randomly chosen client computers serviced by different servers (one per server) will all be infected?
The probability that Alice’s RSA signature on a document is forged is () What is the probability that out of 4 messages sent by Alice to Bob at least one is not forged?
Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible with Event A. What is the probability of getting 6 tails in 10 …show more content…

(Hint: use math expectation)
Let a fair die be rolled n times. Let’s make an assumption that all rolls of a die are independent. If X and Y are the outcomes of any two of n trials, what is the probability distribution of X+Y? That is, create a table that contains each unique possible value of X+Y (each value only listed once) and each possibility’s corresponding probability. We have a fair ten-sided die.
Find the math expectation of a single roll.
Find the math expectation of the numerical sum of 5 rolls.
Find the math expectation of the numerical product (i.e., multiplication) of 7 rolls. are identically distributed independent random variables such that QUOTE and . What is the standard deviation of their average? In other words, what is the standard deviation of ?
If the cumulative distribution function of is given by the function below, then find P (X ≥ 0.75).
, if x ≤ 0 x2, if 0 x ≤ 1 , if x > 1
At the town fair, you can pay $5 to toss a ring at a set of bottles. If you get a “ringer” on the small mouth bottle, you win $50. If you get a “ringer” on the medium bottle, you win $10. If you get a “ringer” on the large bottle, you get your $5 fee back (that is, you break even). If you miss, you are out the $5 you paid to play. Ryan is a good shot and his probability of getting a ringer on the small, medium, and large bottles is 10%, 10%, and 20%, respectively. The probability distribution

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