Find the cumulative density function for the given probability density function. 1 f(x) = 4 for 4 ≤x≤8 F(x)=, for 4 ≤x≤ 8
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- r = 1, ..., n – 1 + r rWhich of the following tables shows a valid probability density function? Select all correct answers. Select all that apply: x P(X=x) 0 0.6 1 0.01 2 0.14 x P(X=x) 0 310 1 110 2 25 x P(X=x) 0 18 1 14 2 58 x P(X=x) 0 0.13 1 0.09 2 0.45 3 0.27 4 0.06 x P(X=x) 0 −15 1 310 2 12 3 310 4 110 x P(X=x) 0 12 1 18 2 38Which statements below are true for a cumulative distribution function (cdf), F(x)? F(x) is a probability. F(x) is non-decreasing. The total area under F(x) is equal to 1. The maximum value of F(x) is 1. F(x) is non-negative.
- The table below shows an incomplete probability density function for X , the number of imperfections per batch of jeans that just came off a production line. What should the missing probability be? Provide the final answer as a decimal. x P(X = x) 0 0.88 1 0 2Alex 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].Determine k so that the function below is a joint probability function. 1 f(x, y) = k(2 − x)(1 −y) 0≤x≤2,0 ≤ y ≤1 {" 0 elsewhere
- Let X be a continuous random variables with with the following probability density function.Answer the following questions.Find the value of α such that f(x) is a probability density function. Make sure thatyou show all the steps.Find the cumulative distribution function of X. Show it on a graph. Make sure thatyou show all the steps.Find the expected value and variance of X. Make sure that you show all the steps.Find the probability density function of Y = X2. Make sure that you show all thesteps.Please answer this one. With complete solution! Thank youVerify Property 2 of the definition of a probability density function over the given interval. 1 10 f(x)= [4,6]
- A 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.) DensityFind k such that the function is a probability density function over the given interval. Then write the probability density function. f(x) = kx, 1≤x≤8 What is the value of k? k = 1 (Simplify your answer.) What is the probability density function? f(x) =Solve using R. Show all work.