University of California, Los Angeles Department of Statistics Statistics 100A Instructor: Nicolas Christou Homework 4 EXERCISE 1 The life of a certain type of automobile tire is normally distributed with mean 34000 miles and standard deviation 4000 miles. a. What is the probability that such a tire lasts over 40000 miles? b. Given that one of these tires has survived more than 30000 miles, what is the conditional probability that it survives for more than another 10000 miles? c. Find the probability that 2 out of 5 randomly selected tires will have lifetime 1 . 96 standard deviations above the mean. EXERCISE 2 Let X be a random variable with probability density function f ( x ) = ± c (1-x 2 ) 2-1 < x < 10 otherwise a. What is the value of c ? b. Find the cumulative distribution function of X ? EXERCISE 3 A filling station is supplied with gasoline once a week. Its weekly volume of sales in thousands of gallons is a random variable with probability density function f ( x ) = c (1-x ) 4
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