# Probability Theory and Random Variable

Topics: Probability theory, Random variable, Cumulative distribution function Pages: 2 (951 words) Published: November 3, 2014

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 trials of tossing a coin? Solve this problem by using :The approximation mentioned in Theorem 6 The Binomial Distribution
Then compare answers for a) and b) after you have solved the problem. When transmitting messages from a point A to a point B, out of every 40 messages 6 need to be corrected by applying error correcting codes. What is the probability that in a batch of 200 messages sent from A to B, there will be between 38 and 42 messages that will have to be corrected? Please choose the appropriate method to approximate this quantity. The probability of an event occurring in each of a series of independent trials is . Find the distribution function of the number of occurrences of in 9 trials. That is, provide a table with all possibilities for number of occurrences of in 9 trials and calculate each’s corresponding probabilities. The probability that a network will be shut down on any given day is 0.0003. What is the probability that the network will be shut down twice in 5000 days? 2 red marbles and 8 blue marbles are placed into a bag. Bob mixes up the bag and randomly selects a marble. He continues to do so, replacing the marble after each selection, until a red marble is selected. What is the probability that the...