Find the cumulutative distribution function of the random variable below given its probability densit
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Find the cumulutative distribution
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- Apple claims that with a fully charged battery, users of its iPhone 11 can stream video up to 10 hours. The minimum battery life for streaming video is 7.5 hours. Assume that for a randomly selected iPhone 11, battery life is uniformly distributed between 7.5 and 10 hours. The density function of this uniform probability distribution is given in the figure below. For values of battery life between 7.5 and 10 hours, the density is 0.4. For all other values of battery life, the density is 0. In the figure above, indicate the probability that a randomly selected iPhone 11 has a battery life between 9 and 10 hours. What is the value of this probability?Suppose that random variable X is uniformly distributed between 5 and 22. Draw a graph of the density function, and then use it to help find the following probabilities:The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.82 and 0.98? (c) What is the probability of generating a number greater than 0.94? ... (a) Choose the correct graph of the uniform density function below. A. В. OC. ADensity 1.2- ADensity 1.2- 1- ADensity 1.2- 1 1. 0.8- 0.6- 0.4- 0.2- 0- 0.8- 0.6- 0.4- 0.2- 0- 0.8- 0.6- 0.4- 0.2- 0+ X 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 0.2 0.4 0.6 0.8 1 1.2 (b) The probability is (Simplify your answer.) (c) The probability is (Simplify your answer.)
- The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.48 and 0.62? (c) What is the probability of generating a number greater than 0.85? (a) Choose the correct graph of the uniform density function below. O A. O B. Density 1.2- 1- 0.8- 6. 0.6- 0 0.2 0.4 0.6 0.8 11.2 0.4- 0.2- to (b) The probability is (c) The probability is Q M (Simplify your answer.) (Simplify your answer.) ADensity 1.2- 1- 0.8- 0.6- 0.4- 0.2- to 0 0.2 0.4 0.6 0.8 1 1.2 Q M O C. 1.2- 1- 0.8- 0.6- 0.4- 0.2- Density 0+ 0 0.2 0.4 0.6 0.8 1 12 Q QA motorcycle drives from Moraytato Lacson and back using the same course everyday. There are four stoplights on the course. Let x denote the number of red lights the motorcycle encounters going from Morayta to Lacson and y denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (x, y) is given by x y 0 1 2 3 4 0 0.01 0.01 0.03 0.07 0.01 1 0.03 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.07 0.1 0.03 0.01 4 0.01 0.06 0.03 0.01 0.01 (g) Give the standard deviation of X. Answer=In a probability density function such as a Normal or bell-shaped curve, the area under the curve is used to make predictions about likelihoods and probabilities. What is the area (use a proportion) under the curve from the lowest possible value to the highest possible value?
- Apple claims that with a fully charged battery, users of its iPhone 11 can stream video up to 10 hours. The minimum battery life for streaming video is 7.5 hours. Assume that for a randomly selected iPhone 11, battery life is uniformly distributed between 7.5 and 10 hours. The density function of this uniform probability distribution is given in the figure below. For values of battery life between 7.5 and 10 hours, the density is 0.4. For all other values of battery life, the density is 0. In the figure above, indicate the probability that a randomly selected iPhone 11 has a battery life between 9 and 10 hours. What is the value of this probability?The figure above shows the probability density function for the random variable x. What is P(3≤x<7)?The random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.27 and 0.85? (c) What is the probability of generating a number greater than 0.92? (a) Choose the correct graph of the uniform density function below. A. B. Density 1.2- 1- 0.8- 606 0.6- 0.4- 0.2- 0 0.2 0.4 0.6 0.8 1 1.2 1.2- 1- 0.8- 0.6- 0.4- 0.2- 0+ Density X 0 0.2 0.4 0.6 0.8 1 1.2 (b) The probability is (c) The probability is to (Simplify your answer.) (Simplify your answer.) X C. 1.2- 1- 0.8- 0.6- 0.4- 0.2- Density 0 0.2 0.4 0.6 0.8 X 1 1.2
- Two six-sided dice are rolled and the scores added together. Draw thesample space, the probability density function and the cumulativeprobability density function by hand. ii. Recent news reports have found that, despite high vaccination rates,around 40% of new positive COVID tests are found in a particular groupof vaccinated individuals. How might Bayes’ Law and the law of totalprobability be useful in thinking about these results? iii. Use either the letters in your surname or numbers in your student idcard to explain the difference between “permutations” and“combinations.” Give a real-world example where the distinctionbetween permutations and combinations is crucial.A Histogram for SO2 emissions data (ton/days with 100 recorded readings is constructed with a width of class interval equal to 5. The maximum frequency is equal to 25 corresponds to class interval 5-20. The probability density corresponding to this interval isThe random-number generator on calculators randomly generates a number between 0 and 1. The random variable X, the number generated, follows a uniform probability distribution. (a) Identify the graph of the uniform density function. (b) What is the probability of generating a number between 0.37 and 0.69? (c) What is the probability of generating a number greater than 0.83? ... OA. В. OC. Density 1.2- A Density 1.2- ADensity 1.2- 1- 1. 1- 0.8- 0.8- 0.6- 0.4- 0.2- 0+ 0.8- 0.6- 0.6- 0.4- 0.2- 04 0 0.2 0.4 0.6 0.8 1 0.4- 0.2- X 0- 0.2 0.4 0.6 0.8 1 1.2 1.2 0.2 0.4 0.6 0.8 1 1.2 (b) The probability is (Simplify your answer.) (c) The probability is (Simplify your answer.) B.
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