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- 3. Let X be a continuous random variable. Let f(x) = c(x − 1)³ and Sx = [1,3]. Hint: (x - 1)³ = x³ + 3x − 3x² - 1 (a) What value of c will make f(x) a valid density? (b) What is P(X = 2)? (c) Find E(X). (d) What is P(1 < X < 2)?8. The density function for the random variable X is f(x). Find E(3X - 1). ) = √(= (2x + 1 (2x + 1) E(3X - 1) = f(x) = 1 < x < 2 0 elsewhere3. Let X be a continuous random variable on the interval [0, 1] having cdf Fx(x) = 3x² − 2x³. Let W = 4 + 3X. (a) What is the range of W? (b) Find a formula for Fw(w). (c) Find a formula for fw(w).
- The density function of two random variables X and Y is fxy (x, y) = 16 e-4 (x+y). u (x) u (y) Find the mean of the function (X, ¥)= 5 for 0 < X s; 1 = -1 for < X and lor< Y 2 = 0 for all other X and YThe 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.1. A continuous random variable X is defined by (3+x) f(x) - 3 sxs- 1 %3D 16 (6-2r) -1sxs1 16 (3-x) -1sxs3 16 a. Verify that f(x) is density. Explain b. Find the mean II
- Let the random variable X have the density function is given by (cx, Os xs5, f(x) = (o, elsewhere. 1) The value of the constant C=; 2) The expected value of X is E(X)=; 3) The expected value of X2 is E(x2) 4) The variance of X is given by Var (X) =0? =.Let X be a random variable with pdf: f(x)= k(10 - 2x) for x being [0,5] a.) Find k b.) Find E(X) c.) Find Var(X) d.) Find E(3 *squareroot(X))Let X and Y be two continuous random variables with joint probability density (3x function given by: f(x,y)=D 0Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
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