1. Assume that the random variable X is the weight of a randomly chosen person from a population. Our goal is to estimate the mean and variance of X so we select 10 person randomly (from that population) and here are their weights in pounds:

150.7,135.3,180,145.2,115.4,232.4,175.3,183.2,155,142.1

Find the sample mean, sample variance and standard deviation.

2)Suppose that waiting time for talking to the customer service (through the phone) for a company follows normal distribution and it has the mean of 6 minutes with the variance of 4 minutes. We assume that the waiting time for each customer is independent of each other.Find the probability that the waiting time for 10 customer is between 50 and 70 minutes?P(50W70)

P(50W70)whereW is the waiting time for 10 customer.

3)Assume that the lifetime of one specific brand ofbattery follows exponential distribution where the parameter is unknown.

In order to test these batteries, we purchased 5 of themand tested them and here is their lifetime:4,2,3, 1and 2 years.

Calculate the maximum likelihood estimation for the parameter