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Question 1 4 pts Suppose that 5 cards are taken with replacement from a deck of 52 cards, and r.v. X is the number of red card you get, then 1. expected value of X is 2. variance of X is 3. P(X=1) = 4.P(X 2 3) = Remind : keep your answer as 2decimal number Question 2 3 pts Suppose that 5 cards are taken without replacement from a deck of 52 cards, and r.v. X is the number of red card you get , then 1. expected value of X is 2. variance of X is 3. P(X=1) = Remind : keep your answer as 2decimal number Question 3 4 pts Suppose that the number of errors in a piece of software has a Poisson distribution with parameter A =4. 1. What is the probability that a piece of software has no errors? 2. What is the probability that there are at least one errors in a piece of software 3. Find the expected number of error. 4. Find the variance in the number of errors. Remind : keep your answer as 2-decimal number M Inbox ( M Inbox ( UNC CI| Final Le Grades DX Mathw Files Probab Qui X S Solution Please Ask ac f Chegg + X G G Update Apps Anusha Reading list D Question 4 4 pts unt When pearl oysters are opened, pearls of various sizes are found. Suppose that each oyster contains a pearl with a bard diameter in mm that has a U(0, 8). 1. Find the probability that diameter of the pearl in the oyster is ses between 2 mm and 8 mm. ips 2. Find the probability that diameter of the pearl in the oyster is at least 5mm. dar 3. Find the expected value for the diameter of the pearl. 5 4. Find variance for the diameter of the pearl. ory Remind : keep your answer as 2-decimal number Type here to search O BOR 9 2:55 PM 90 OF 6/29/2021Question 5 3 pts Suppose that you are waiting for a friend to call you and that the time you wait in minutes has exponential distribution with parameter /\\ = 0.2 . 1. What is the probability that you can receive the call within 5mintes? 2. What is average time you need to wait? 3. If after 5 minutes, you are still waiting for the call, your additional waiting time also has Exponential distribution with parameter A = 0.2. (True Or False) Remind : keep your answer as 2-decimal number