9. For the probability density function given in Problem 7, (a) Graph this function. What would be a good name for this distribution? (b) Compute P (≤x<1). 7. Let X be a continuous random variable and let α-1 f(x) be its probability density function. For what values of a does E(X) exist?
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- 10) Let f(x) by the probability density function of some continuous random variable. Explain why it must be true that f(x) dx =1.5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = I > 0 (x+0)a+1³ is a probability density function. What can you say about the mean of a random variable that has fo,a as a pdf?Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?
- Let X be a random variable with probability density function 3 f(x) = ,a², –1 < = <1 2 Which of the following is the probability density function of Y = X – 1?Let X be a random variable with pdf f(x) = kx*,-1The continuous random variable X has the following probability density function: Ax, 0Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X be a random variable with probability density function [ a + bx², 0A random variable X has probability density function (x² + 2x + 4) for 0 < x < 3 f(x) = otherwise. Which of the following gives the cumulative distribution function F(x)?7. Let X be a continuous random variable with probability density function given by Se-(2-z0) f (x) = x > x0 x < xo Find E(X).The probability density of the random variable Z isgiven by f(z) = kze−z2for z > 00 for z F 0Find k and draw the graph of this probability density.Let X be a random variable with discrete pdf f(x) = x/8 if x = 1, 2, 5, and zero otherwise. Find: (a) E(X).SEE MORE QUESTIONSRecommended textbooks for youGlencoe Algebra 1, Student Edition, 9780079039897…AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
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