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Assignment No: 2 (Lessons 28-30)
Question 1: Marks: 4+4=8
a) Suppose 4 dresses are randomly chosen without replacement from the total of 8 dresses (5 red and 3 white). Calculate the probability of getting exactly 2 red dresses out of 5 red dresses. (Solve using hypergeometric distribution)
b) A random variable “X” following binomial distribution with n=5 and p=0.5 Calculate the mean, variance and Coefficient of Variance.
Question 2: Marks: 4+3=7
a) One hundred passengers have made reservations for a train. If the probability that a passenger who has a reservation will not show up is 0.01, what is the probability that exactly 2 will not show up? (Use appropriate distribution)
b) A certain type of car battery lasts on an average 2 years, with a standard deviation of 0.5 year. Assuming that the battery lives are normally distributed, find the probability that a given battery will last less than 2.5 years.
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