The mean was given to be  ? = 11  and  x0 was determined to be 11. Substitute these values into the formula for the cumulative probability to find the probability that arrival time between vehicles is 11 seconds or less, rounding the result to four decimal places. P(x ≤ x0) = 1 − e−x0/? P(x ≤ x0) = 1 − e(-11/11) P(x ≤ x0) = ?

Newell et al. 2022 observed the following relationship between precipitation p (measured in mmrainfall) on the abundance of arthropods A (measured in mg/m2 biomass) in Peru. I provided an image of the equation below (a) On what intervals does increasing precipitation increase biomass? (b) On what intervals does increasing precipitation decrease biomass? c)At what rate does increasing precipitation increase/decrease biomass in a rain forest thatreceives 500mm of rain annually?

Highway engineers use f(x) = (0.905)* to estimate the likelihood, or probability, that no vehicle will enter a particular intersection within an interval of x seconds. Construct a table of f(x) = (0.905)* starting at x = 0 and incrementing by 10, until x = 50. a. Evaluate f(1) and interpret the result. b. For a time interval of what length is there only a 2% chance that no cars will enter the intersection?

The life X (in years) of a voltage regulator of a car has the pdf: X 3 - (-/-)². 3x2 73 0≤x≤∞ What is the probability that this regulator will last at least 7 years? Give your answer to 3 decimal places and show working.

The frequency of earthquakes in an area recorded over time can be modeled using the exponential function, given by x 2 0 f(x) 0, x< 0 where x is the earthquake's Richter magnitude scale and 2 is a constant. If 2 = 1.75 and letting x be the random variable indicating the earthquake's strength, answer the following questions: How frequent do earthquakes of less than Magnitude 1.0 occur compared with earthquakes of Magnitude 1.0-2.0? What is the probability that the next earthquake event has a strength greater than Magnitude 8.0? What is the expected value of the random variable а. b. с. х? d. What is the standard deviation of the random variable x

The 2010 U.S. Census found the chance of a household being a certain size. The data is in the pmf below ("Households by age," 2013). Let X be the number (size) in a household. E(X) = k·P(X = k) 7 (or more) P(X=k) 0.267 0.336 0.158 0.137 0.063 0.024 0.015 k 1 2 3 5 6 a) The probability of a household size being more than 5, P(X > 5) = % b) In the long run, we are expected to see a household size of, E(X)= on average. Round answer to three decimal places. c) The probability that the size of a household is equal to two is %. d) The probability of a household size being three OR six is %.

You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly different from 63%. With H, :p 63% you obtain a test statistic of z = - 1.222. Find the p-value accurate to 4 decimal places. p-value =

Assume x is exponentially distributed with a mean of 4. Find: a.P(X=2) b.P(X<2) c.P(X>=2) d.P(2 < X < 4)