The lifetime T (this year) for a particular type of electric toothbrush is assumed to have the probability density f given by 1 t 0 < + < 6
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- In Minecraft, about 5 zombies will spawn every minute. Define X as the waiting time in minutes for the first zombie to spawn. The probability density function is then given by f (x) = 0, x > 0 x < 0 Find the CDF, F(x). Write your answer as a piecewise function.The lifetime T(in years) of a device is given by the probability density function in the picture below. Two students are asked to find t=L. Please help find which student had the right setup to find L with work. Either one, both, or neither.A scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the camp has probability density function f(x) = VT, 0< x < 1. 0 < x < 1. According to the model, what is the mean length of the sticks that the scout brings back?
- 2. Consider a gas station's daily sales. Let Y be the volume of gas sold per day in 1000s of gallons. Assume the distribution of Y follows this pdf: 1sxs 2 S (v) . else What value of k is required for the above function to be a valid pdf? b. Verify that the function given is a valid probability density а. function c. Determine the cumulative distribution function (cdf) of the random variable d. Compute the probability that there is exactly 1500 gallons of sales on a given day (Hint: Find?(r - 1.5)) = 1 CO0The table below shows a probability density function for the discrete random variable X, the number of misspelled words that an editor finds per page in a novel. What is the probability that X is 0, 1, or 4? Provide the final answer as a fraction.According to a study, the maximum temperature T (in degrees Celsius) of each day during the spring has a distribution with the following function density: 21The graph shows the uniform density function for a friend who is x minutes late. Find the probability that the friend is at least 15 minutes late.The continuous random variable X has the probability density function (pdf) given by: (k - 5+x f(x)=- 5For the probability density function f defined on the random variable x, find (a) the mean of x, (b) the standard deviation of x, and (c) the probability that the random variable x is within one standard deviation of the mean. 1 f(x) = x, [5,9] 28 a) Find the mean. %3D (Round to three decimal places as needed.) b) Find the standard deviation. (Round to three decimal places as needed.) c) Find the probability that the random variable x is within one standard deviation of the mean. The probability is. (Round to three decimal places as needed.)The service life T (this year) of a particular type of electric toothbrush is assumed to have the probability density f given by: see figure question (a) Find the probability that a randomly selected toothbrush (of this type) has a lifespan of more than 2 years.(b) Assume that a toothbrush of the same type has been working for one year already. What is the probability that it works for at least another 3 years?(c) What is the probability that the average lifespan of T¯ for 90 independent toothbrushes is greater than 2.1 years?Consider the following constant function: f(x) = 3/4 If this function represents a probability density function, which of the following can be a set of realized values? A. 2/3 ≤ x ≤ 2 B. 1/4 ≤ x ≤ 1 C. 3 ≤ x ≤ 4 D. 1/2 ≤ x ≤ 3/2A scout on a camping trip is requested to find some dry sticks of length at most one metre to use as firewood. A model for the distribution of the lengths, X, in metres, of sticks that she brings back to the probability density function camp has f (x) =V, 0 < x < 1. %3D According to the model, what is the standard deviation of the lengths of the sticks that the scout brings back?Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON