Probability Density Functions II 1. A real number is selected at random from the

Question

Probability Density Functions II 1. A real number is selected at random from the interval (0,100). What is the probability that it is an integer? Transistors produced by a machine have a lifetime, which is a continuous random variable having a PDF which is approximately exponential with -200 hours. Let X be the lifetime of a randomly selected transistor produced by this machine. 2. Give a formula, f(x). Find the probability that a random transistor will last more than 200 hours. Find the probability that a random transistor will last between 100 and 300 a. b. c. hours. d. Find a formula for F(x). e. What is F(500)? Find and . Assume that cans of Pepsi are filled by a machine so that the actual amounts have a normal density with mean of 12 ounces and a standard deviation of 0.2 of an ounce. 3. a. Give a formula for the above density b. Find the probability that a random can of Pepsi will contain between 11.9 and 12.3 oz. c. Are there any significant differences between the theoretical limits of this normal density and actual limits? d. One percent of all cans are expected to exceed x oz of soda. Find x . A controlled satellite is known to have an error (distance from target) that follows a normal density with mean zero and standard deviation ten feet. The manufacturer of the satellite defines "success" as a launch in which the satellite comes within 25 4. feet of its target (if the satellite reaches its intended target the error is zero). What is the probability that when launched, a random satellite will succeed? a. What would have been the probability of failure had the standard deviation been 20 feet instead of 10? b.

Explanation / Answer

Ans 1.

Total integers between (0,100) = 99

Total real numbers between (0,100) = infinity

Total prob = 99/infinity = 0

PS: We are directed to solve only first if multiple questions are posted

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