2) Let the joint probability function of X & Y be defined by Pxx (x, y) = x= 1,2 y = 1,2,3 Find E(X+Y). Find Pxy (xly). What is Pxy (x2)? What is Px|y (212)? Find Py|x (vlx). What is Pyx (12)? What is Py|x (212)?
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- If X has an exponential distribution, show thatP[(X Ú t + T)|(x ÚT)] = P(X Ú t)A gasoline station gets its supply once a week. Suppose the PDF of X = demand in thousands of gallons for gasoline is: fx(x) = 5(1 – x)*I(0.1)(x) a. What is the probability that the demand for gasoline in a given week is more than 500 gallons? b. How much gasoline must the station get from its supplier in order for the probability that its supply will be exhausted in a given week shall be 0.01?gn X Three couples and two single individuals have been invited to an investment seminar and have agreed to attend. Suppose the probability that any particular couple or individual arrives late is 0.41 (a couple will travel together in the same vehicle, so either both people will be on time or else both will arrive late). Assume that different couples and individuals are on time or late independently of one another. Let X = the number of people who arrive late for the seminar. (a) Determine the probability mass function of X. [Hint: label the three couples #1, #2, and #3 and the two individuals #4 and #5.] (Round your answers to four decimal places.) P(X = X) X 0 1 2 3 4 5 6 7 8 (b) Obtain the cumulative distribution function of X. (Round your answers to four decimal places.) F(x) X 0 1 2 3 4 5 6 7 Use the cumulative distribution function of X to calculate P(2 ≤ x ≤ 5). (Round your answer to four decimal places.) P(2 ≤ x ≤ 5) = Need Help? Read It Watch It 4
- Individual A has a red die and B has a green die (both fair). If they each roll until they obtain five "doubles" (1-1,...,6-6), what is the pmf of X (= the total number of times a die is rolled)? What are E(X) and V(X)?If E[X] = 1 and Var(X) = 5, use definition of variance and properties of expectation to find (a) E[(2 + X)^2] (b) V ar(aX) for any constant a. (c) V ar(X + b) for any constant b. (d) V ar(4 + 3X)Because P(A n B) has been defined as x, and we calculated the value of P(An B) = P(A) · P(B) to be x² + 0.49x + 0.058, we now solve for x, the probability of both pumps failing. P(A n B) = P(A) · P(B) x = x² + 0.49x + 0.058 0 = : x² - ( Solving the quadratic equation for x results in two values that represent the possible probabilities that the pumping system will fail on any given day. Rounding both values to four decimal places, the lower value is x = the larger is x = |× )×· + 0.058 , and