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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- Verify that the function corresponding to the following figure is a valid probability density function. Then find the following probabilities: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?A random variable X has density 3x2 for 0 < x < 1. Find its variance.(use a decimal number, rounded to the nearest 1,000th. For example, 0.123)
- 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 QIn 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 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 0.63 and 0.76? (c) What is the probability of generating a number greater than 0.83? (a) Choose the correct graph of the uniform density function below. A. В. ADensity 1.2- ADensity 1.2- 1- 0.8- 0.6- 0.4- 0.2- ADensity 1.2- 1. 0.8- 0.6- 0.4- 0.2- 0+ 1 0.8- 0.6- 0.4- 0.2- 0+ X X 0- 0 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 0.27 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