1. Suppose X has probability function f(x)= x/6 x=1, 2, 3 Find g(y) if Y=X²
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A: Sample is subset of population, while population is entire set.
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A: The number of households is 411.
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A: b) The regression equation is y^=31-2x.
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A: data in accending order 61,66,67,67,68,73,74,75,75,75,82,85,86,89n = 14
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- Repeat Example 1a for the function f(x)=2x2 on [1,2]. What is the probability that X will be between 32 and 2?5. Why the probability P(X=x)=0, for a continuous variable,?9) The effectiveness of solar-energy heating units depends on the amount of radiation available from the sun. During a typical October, daily total solar radiation in Tampa, Florida, approximately follows the following probability density function (units are in hundreds of calories): 3 f (x) ={32 (x- 2)(6-x) for210. Suppose the probability of selecting a number from the interval [0, 2] is given by f(x) = Cx. (a) Find the value of C so that this is a probability distribution. (b) Find the probability that the given number is in the interval [0,1]. Now find the probability that the selected number is in the interval [1, 2]. The answers differ. Why? (c) If X (x) = x is the random variable giving the value of the selected number, what is E(X)? The Var(X)?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?(4) If a point x is taken at random on the interval [0, 2a] and all the points are equally likely to be taken, the probability that the product x(2a-x) > isIf the joint probability distribution of X1 and X2 isgiven by f(x1, x2) = x1x236for x1 = 1, 2, 3 and x2 = 1, 2, 3, find(a) the probability distribution of X1X2;(b) the probability distribution of X1/X2.2. For the following discrete variable with probability f(x) X 1 2 3 4 5 f(x) 0.2 0.15 2c 0.05 0.15 РX 3) Select one: О а. 0.65 O b. 0.3 O c. none O d. 0.77. Consider the function P(x) 12 for x = 1, 2, 3 and 4. What is the probability that x is 25x between 1 and 4? а. 1 b. 2/5 С. 6/25 d. 4/25 e. 12/53. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.There are only two states of the world, when a person is well with probability (1-p) and ill with probability p, where (1-p)= 1/3 and p = 2/3. Consider Adam who has utility function U = (Y1, Y2,1 – p,p) = Y,"-P)Y?, where Y; is the income and i =1 is well and i = 2 is ill. When Adam is well, he earns $1000, but when he is ill, he losses $300 in health expenditures and earnings such that Y2 = $700. What is the maximum total premium that Adam is still willing-to-pay? (1-р).Consider the three functions I. f(x)= {1-x if 0 < x < 2 {0 otherwise II. f(x)= {1+x if 0 < x < 2 {0 otherwise III. f(x)= {(3/27)x^2) if 0< x < 3) {0 otherwise Which of these above functions can be probability distributions? And why?SEE MORE QUESTIONS
