7. Which of the following is/ are true? (3 marks) . Response to this question requires at least one option. For a binomial distribution with a large number of trials and a small probability of success, Poisson distribution can be used to approximate the binomial distribution. [conditions: n is at least 20, p is at most 0.05 and np 5 and nq > 5] When we use a continuous distribution to approximate the probability of a discrete random variable, the continuity correction (+ 0.5) can be applied to improve the approximation. We need to apply continuity correction (+ 0.5) when we use Poisson distribution to find the probability of a binomial random variable.Default Section 1. The number of successes is the random variable for this distribution. Choose all that apply. (2 marks . Response to this question requires at least one option. Binomial distribution Negative binomial distribution Bernouli distribution Geometric distribution 0 Possion distribution O Hypergeometric distribution . The number of trials is the random variable for this distribution. Choose all that apply. (2 marks) . Response to this question requires at least one option. O Bernoulli distribution O Binomial distribution O Negative binomial distribution Geometric distribution 0 Poisson distribution. Hypergeometric distribution. 3. Fill in the blanks (5 marks) . Please fill in all the blanks for this question. If the probability of success is 0.2 in any given trial, and X is the number of successes out of 5 (independent) trials, Find 1) The expected number of success = 2) The expected number of failures = 2 3) The variance of X = 3 (leave your answer to 1 decimal places) 4) The standard deviation of X = 4 (leave your answer to 3 decimal places) 5) The probability that X = 0, that is the probability of observing NO successes = 5 (leave your answer to 5 decimal places) Enter the correct answer below. lease enter a number for this text box. 2 Please enter a number for this text box. 3 Please enter a number for this text box. A Please enter a number for this text box. 5 Please enter a number for this text box. Character Limit: 74. Fill in the blanks {3 marks) If the probability of a success Is 05 for any given trial, and X follows a negative binomial distribution with 3 successes. Find \"The expected value ofX= 1 2} The variance of X = 2 3) The probability that 5 trials are required to achieve 3 successes = 3 (leave your answer to 4 decimal places} Enter the correct answer below. 1 Please enter a number for this text box. 2 Please enter a number for this text box. 3 Please enter a number For this text box. 5. Fill in the blanks {2 marks) Let X be the number oftypographlcal errors found on a page. It Is known that X follows a Poisson distribution with the average number oferrors of5 per page. \"The variance of X = 1 2) The probability of NO successes = 2 (leave your answer to 5 decimal places) Enter the correct answer below. 1 Please enter a number for this text box. 2 Please enter a number for this text box. 6. Fill in the blanks [3 marks) If X follows a discrete uniform distribution, and the possible values of X are: 10, 20, 40 and 50, find \"The probability mass function {p.m.f.] ofeach possible value of x. P.m.f. of X = i (leave your answer to 2 decimal places) 2) The expected value of): = 2 3} The variance of X = 3 Enter the correct answer below. 1 Please enter a number [or this text box. 2 Please enter a number [or this text box. 3 Please enter a number [or this text box