Given the following probability density function x² 0
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- Alex decides to sell his old guitar, and sequentially receives bids from potential buyers. The minimum price that he will accept to sell his guitar for is £500. Let {Xn, n ≥ 0} denote the sequence of independent and identically distributed bids that Alex receives, and assume that each Xn has the following probability density functionfX(x) = (1/400)e-x/400 for x ≥ 0. Let N denote the number of bids that Alex obtains before selling his guitar i.e., Alex sells his laptop to the Nth bid. Showing your full working, (a) find E[N]. (b) find E[XN].Show the solution and answer for this problemConsider the following exponential probability density function. a. Which of the following is the formula for P(x ≤ xo)? 1 P(x ≤ xo) = e TO Formula #2 20 2 P(x ≤ xo) = 1-e 3 P(x ≤ xo) = 1-e-20 b. Find P(x ≤ 1) (to 4 decimals). c. Find P(x ≥ 4) (to 4 decimals). 0.3679 d. Find P(x ≤ 6) (to 4 decimals). 0.7769 e. Find P(1 ≤ x ≤ 6) (to 4 decimals), 1 f(x) = = e h for 20
- Find the value of k for which the following function would be a valid probability density function f(x)=k(x²+1) with 1 ≤x≤4 or f(x) =0 of which is otherwise a. Calculate P(x=3) b. Calculate P(2 ≤ x ≤ 3)Let X will be continuous random variable with probability density function as below. f(x) ={0, otherwise S4x3 (0Chen Construction Company is bidding on a job. For ease of calculation, let's assume the actual construction cost is $0. One other company is bidding for the job. Suppose the opponent is going to bid x million dollars. Chen believes that x has the following probability density function (pdf): 2x, if 0A sample of women's heights was taken. Their heights (in inches) are defined by the following probability function. 0.0825x5.0325 for 61 < x < 65 f(x) = -0.0425x + 2.9325 0 for 65 ≤ x < 69 elsewhere The graph of f(x), the density curve, is shown below. 0.35 0.30 0.25 0.20 A 0.15 0.10 0.05 0.00 61 62 63 64 65 66 67 68 69 Height Part 1 of 3 Find the probability that a randomly selected woman from the sample has a height greater than 67 inches. (Round your answer to three decimal places.) DensityWhich of the following is NOT a valid probability density function? O 0.04x 0.4-0.04x f(x) = 0 for 01. Consider a random variable X with probability density function given as: 0 if x < 0, 1 if 0 ≤ x ≤ 1, f(x) 2 1 if 1 < <∞. -2x² Verify if f(x) is indeed a density function. If it is, find the distribution function of X.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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