(a) What is the interval of possible values for X? (b) Find the formula for the density function f(x) of X. (c) Find the mean and variance of X (do not compute any integrals).
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- The wait T in hours between every phonecall a person recives is random given the densityfunction f(t) = 1.8e-1.8t for t ≥ 0 Find the expected time between calls and find the variance.Let X have the density function 2x /k2 if OConsider the random variable X with PDFf(x) = e−x / (1 + e−x)2 , x ∈ R.Find the density function of Y = 1/ (1 + e−X)A teacher wants to estimate the mean time (in minutes) that students take to go from one classroom to the next. His research assistant uses the sample time of 36 students to report the confidence interval as [8.20, 9.80]. (You may find it useful to reference the t table.) a. Find the sample mean time used to compute the confidence interval. (Round final answer to nearest whole number.) probability= (ANSWER IS NOT 0.005 or 0.1)Let X and Y be two random variables with joint density function f(x,y) = (3 − x + 2y) / 60, for 1 < x < 3, 0 < y < 5. Find the marginal density functions. (Check that they are nonnegative and integrate to 1 before continuing further) Are X and Y independent? Explain.Continuous variable X is distributed on the interval [b,c] = [24.4, 64.6] according to the density curve shown below. As indicated by the plot, the distribution of X is symmetric. What is the mean of this distribution equal to? If there is not enough information to answer this question, enter 0 below. Otherwise, enter the value of the mean. f(x) b сLet X1, X2, . X6 be an i.i.d. random sample where each X, is a continuous random variable with probability density function f(x) = e-(-0) , x > 0 Find the probability density function for X(6).Consider a group of people who have received treatment for a disease such as cancer. Let t be the survival time, the number of years a person lives after receiving treatment. The density function giving the distribution of t is p(t) = Ce-Ct for some positive constant C, and the cumulative distribution function is P(t) = , p(x)dx. Think carefully about what the practical meaning of P(t) is, being sure that you can put it into words. a) The survival function, S(t), is the probability that a randomly selected person survives for at least t years. Find a formula for S(t). b) Suppose that a patient has a 80 percent chance of surviving at least 2 years. Find C. c) Using the value of C you found in (b), find the probability that the patient survives up to (that is, less than or equal to) 1 years. d) Using the value of C you found in (b), find the the mean survival time for patients with this survival function, in years.he length of time, in minutes, for an airplane to obtain clearance for takeoff at a certain airport is a random variable Y = 3X-2, where X has the density function. Find the mean and variance of the random variable Y.The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8ANSWER IN 10 MINUTES PLEASEEEE, Probability and Statistics for Engineers and Scientists 1- Let X and Y be two independent random variables. If the variance of X is 13 and the variance of Y is 8, find the variance of the random variable Z = 2X + 3Y 2- A continuous random variable X has the density function f(x)=k/(x^2), if M<x<M+1,and f(x)=0,elsewhere. If M=48, find the value of k.2.5 Y has a density function S0) = (2 y), 0 < y < 2 elsewhere Find the mean and variance of Y.Recommended 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