The probability density function for continuous random variable, x, is given above. P(x P(x = 1.5) =
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- Choose the correct answerLet X be a random variable with density function f(x) = { k(1-x²), if 0≤x≤ 1; otherwise. Find k, together with the expectation and the variance of the random variable Y defined as Y = 3X - 1. fandThe cumulative distribution function of a continuous random variable X is given as Choices: A. 0.4 B. 0.5 C. 0.6 D. 0.7 E. 0.8 F. 0.9 G. Other:
- Derive the moment generating function (MGF) of a random variable ?.A random variable X has density 3x2 for 0 < x < 1. Find its variance.(use a decimal number, rounded to the nearest 1,000th. For example, 0.123)In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x is 1 2 p(x) 0.3 0.6 0.1
- The table below represents the probability density function for the random variable X. Find the standard deviation of X. Round the final answer to two decimal places. x P(X = x) 1 1/4 3 1/4 4 1/2For a random variable which can be defined using the probability density function below, what is the probability that X is between 1.5 and 3.2? f(x) = {C(1+ x) ,1Find the mean and variance of X given the following probability density function:The table below represents the probability density function for the random variable X. Find the standard deviation of X. x P(X = x) 0 1/6 1 1/6 4 1/3 7 1/3Suppose that the probability density function of a random variable X is as follows: f(x)= cx, for0<x<4; 0, otherwise. (a) Find c.(b) Find the cumulative distribution function F and sketch it.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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