Unit 5 In-Class Exercise Apple claims that internet use. The minimum battery lif
ID: 3045201 • Letter: U
Question
Unit 5 In-Class Exercise Apple claims that internet use. The minimum battery life is 9.5 hours. Assume that for a randomly selected one X, battery life is uniformly distributed between 9.5 and 12 hours. The density function of this uniform probability distribution is given in the figure below. Density Punction of Battery Le battery lide For values of battery life between 9.5 and 12 hours, the density is 0.4. For all other values of battery life, the density is 0. For a randomly selected iPhone X, what is the probability that the battery life is larger than 11 hours? Indicate this probability in the figure above, and calculate it. 1. 2. Calculate the probabilities that (i) the battery life lies between 9.5 and 10 hours; and (ii) the battery life is less than 10 hours. Are these two probabilities different? Explain why or why not. What do you think the expected value of the battery life is?Explanation / Answer
(a) The maximum value that the battery life can take is 12 hours. So, basically what you need to do here is integrate the probability function between 11 and 12, but since this is a uniform distribution, you can just simply calculate area of the rectangle under the curve between X=11 and X= 12, ie.
lenght * breadth
(12-11) * 0.4 = 0.4
(b) again by the same logic, this will be:
(10-9.5)* 0.4 = 0.2
Both the probabilities will be the same, because, the battery life cannot be less than 9.5 hours.
(c) So, this will just be the average battery life, so the mean of 9.5& 12 = (9.5+12)/2 = 10.75 hours
Thankyou
= 0.4
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