For the random variable X with the density function f(x) = = compute E(ex). 3e -3x 10 for 0 < x < ∞ otherwise
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- Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X + 25. Then what is the probability density function of Y (fy(y)). Probability TheoryLet Y be a continuous random variable with √ ½ (2 f(y) = = Find the mean (u) and variance (o²) of Y. (2−y), 0≤ y ≤ 2 elsewhere.Let Y be a continuous random variable. Let c be a constant. PROVE Var (Y) = E (Y2) - E (Y)2
- Suppose X and Y have joint probability density function f(x, y) = { 0(a C(x² + y²), if 0Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = x2 – 10X + 25. Then what is the probability density function of Y (fy(y)).Suppose that Y is a continuous random variable. Show EY yfr(y)dy.1. A continuous random variable X is defined by (3+x) f(x) - 3sxs-1 %3D 16 (6-2r) -1sxs1 16 (3-x) -1sxs3 16 a. Verify that f(x) is density. Explain b. Find the mean 2. If the probability density function of random variable is given by f(x) = wch 1srs2 sech x a. Find the mean b. Find the total area 3. If the probability density function of random variable is given by f(x) = sinh 2x 1sxs2 a. Find the mean b. Find the total area c. Illustrate the graph (use bell shaped figure) II II1. 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 IILet X1, X2, ..., Xn be a random sample from a population with probability density function 4 - 33 √T.² Find a sufficient statistic for 3. Justify your answer. f(x) = 0 < x <∞.The pH water samples from a specific lake is a random variable X with probability density function. f(x) = {8 (7– x)², 5 < x<7 0, elsewhere a. ) Find E(X) ( expected value or mean) b. ) Find V(X) ( Variance)Recommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,