Suppose that a random variable X has PDF defined by fx(x): = a(1+x) a(1-x) 0 if −1 < x < 0 if 0 b] = / P[X ≤ b].
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- Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X denote the temperature at which a certain chemical reaction takes place. Suppose that X has pdf f(x)={1/9(4-x^2) -1<=x<=2 0 otherwise a) Compute P(0≤ X ≤1)b) Obtain E(x) and Variance of XLet f(x, y) = x + y for 0 < x < 1 and 0 < y < 1 The Conditional Variance of Y when X = ; is
- The random variable X has PDF given by 1 f(x)=√e-2/4 -x/4 for x > 0, zero otherwise. Compute P(X> 5) rounding to four decimal places.Suppose X is a random variable, whose pdf is defined as follows: 2x = (²x) (u(x) - u(x − 3)) where u(x) is the unit step function. Determine the conditional pdf fx(x 1Let X1, X2,..., Xn be a random sample from a population with a pdf a+2022 (a+ 2021) („) ;x > 0, a > 0 x+1 f (x) 0, elsewhere. II n 1 Show that | is sufficient for a. X; +1Let X be a random variable with pdf f(x) = kx*,-1Let the random variable X be the time in seconds between incoming telephone calls at a busy switchboard. Suppose that a reasonable probability model for X is given by the pdf: fx(x) = { ie for 0Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable—X for the right tire and Y for the left tire, with joint pdf f(x, y) = K(x2 + y2) 19 ≤ x ≤ 29, 19 ≤ y ≤ 29 0 otherwise (a) Determine the conditional pdf of Y given that X = x. fY|X(y|x) = for 19 ≤ y ≤ 29 Determine the conditional pdf of X given that Y = y. fX|Y(x|y) = for 19 ≤ x ≤ 29 (b) If the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi? (It is known that K = 3 350,600 . Round your answer to three decimal places.) Compare this to P(Y ≥ 25). (Round your answer to three decimal places.)P(Y ≥ 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = 3 350,600…Recommended textbooks for youBig Ideas Math A Bridge To Success Algebra 1: Stu…AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtBig Ideas Math A Bridge To Success Algebra 1: Stu…AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt