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- 2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, 1.-/9 f(t) = V9T This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t a andt = b. A related function is %3D F(x) = -2/9 dt, 2 0. %3D V9n Jo This function gives the probability that the day's temperature is between t = -x and t = x different from the monthly average temperature. For example, F(1) 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the…2. An investor's losses follow a distribution with density function, f(x) =, x > 1 and 0 everywhere else, To recover her losses, the investor purchases an insurance policy with a deductible of $1. Show that the insurance company will go bankrupt. Hint: The expected amount of the losses paid by the company is too large.I want solutions of all these examples.
- 3. Given the cumulative distribution function of a continuous variable X, 0, x < 0 -fire Ax², 0Q 3. (a) If the joint probability density function of X and Y is given by | 24:ry for 0 0.27. If the joint density of the random variables X and Y is [emin{x,y) - 1] e-(x+y) if 0 < x, y <∞ f(x, y) = 0 otherwise, then what is the marginal density function of X, where nonzero?3. Assume that the survival function for hippogators is given by 100 - 2² 100 for 0 ≤ x ≤ 10. (a) What does this imply about s(x) for x > 10? (b) Determine the cumulative density function and the probability density function for the com- plete lifetime for a hippogator of age 2. s(x) = (c) Construct a life table for these hippogators including lz, dz, Pz and qe for ages 0 ≤ x ≤ 4 Use a radix of lo = 1000 and give non-integer entries to 3 decimal places. (d) What is the probability that a hippogator of age 4 lives to age 6 but dies by age 9?11. (5 Percentages on a professional entrance exam are described by the probability density [cy² (1-y), 046. Given that X has a density function 2x 3- x f (x) = for 05.Suppose X is a continuous variable with density function (3,2 f(x) ={2" .-l12. A branch of a certain bank in Davao City has six ATMS. Let X represent the number of machines in use at a particular time of day. The cumulative density function of X is as follows: x 3) c) P(2Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSONA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON