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- Let μx and of be the expectation and variance of a forecast model F for an observations y, and let pÃ(.) denote the probability density function for the forecast model. Also let G be a different forecast model. Which of the following statements are true? a. Two forecast scores S(F, y) and S(G, y) are independent. b. The square error (y – µµ)² is a proper score. C. The score (y - μF) ²/0 is proper score that improves in the squared error score by taking the variance into account. d. The logarithmic score – log[pf(y)] is a strictly proper score. -The graph to the right is the uniform probability density function for a friend who is x minutes late (a) Find the probability that the friend is between 5 and 25 minutes late (b) it is 10 AM. There is a 30% probability the friend will arrive within how many minutes? (a) The probability that the friend is between 5 and 25 minutes late is (Type an integer or a decimal Round to three decimal places as needed.) (b) There is a 30% probability the friend will arrive within minutes (Type a whole number) Ang 100 10 20 30x TemIn 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.
- Ex 2/ Let X be exponential random variable with parameter A = 1:5. Find: 1- Find the probability distribution function 2- F[X] ? 3- E[X*) ? 4- Var(X)? 5- Find standard of deviation of X?3) The probability density function is f(x) = 2e¬kx X>0 Find the value of k.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 CO0
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