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Text messages arrive at a cell phone at a mate 2 messages per minute. The arrival of text messages occurs at random times according to a Poisson scatter on (0, co). Show all your work for each part. a. What is the probability that no text message arrives between { = 0 and ( = 30 seconds? b. What is the probability that the third text message arrives after / = 3 minutes? c. What is the probability that the 5-th text message arrives within 1 minute of the 4-th text message? d. What is the probability that the 1-st text message arrives in less than 1 minute and fewer than 2 text messages arrive between ( = 3 and f = 5 minutes. e. What is the expected waiting time for the 20th text message?Text messages arrive at a cell phone at a mate 2 messages per minute. The arrival of text messages occurs at random times according to a Poisson scatter on (0, co). Show all your work for each part. a. What is the probability that no text message arrives between { = 0 and ( = 30 seconds? b. What is the probability that the third text message arrives after / = 3 minutes? c. What is the probability that the 5-th text message arrives within 1 minute of the 4-th text message? d. What is the probability that the 1-st text message arrives in less than 1 minute and fewer than 2 text messages arrive between ( = 3 and f = 5 minutes. e. What is the expected waiting time for the 20th text message