16 Find the expected value of the function g(X) =X², where X is a random yariable defined by the density function Sxlx) = a e¯ ar u(x), where a is a constant
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- Let x be a continuous random variable with the density function: f(x) = 3e-3x when x>0 and 0 else Find the variance of the random variable x.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 TheoryThe 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 Y
- 1) Let x be a uniform random variable in the interval (0, 1). Calculate the density function of probability of the random variable y where y = − ln x.Be X a random variable with density function defined by f(x) = -2², , x>0. 3 Get the moment-generating function and based on it, calculate the average and variance of X.Let Y be a continuous random variable with a probability mass function: f (y) = Derive the moment generating function (MGF) of a random variable Y.
- A random variable has density function f(x) = 1.6 - 1.2x, for 0≤ x ≤ 1. a) Calculate the variance of X. Var(X) = 0.4 b) Calculate the variance of g(X) = 4X + 1. Var(g(X)) = XA continuous random variable X has density function f(x) = 1.5(1 – x²), 0 < x < 1. a) Calculate the expected value of X. b) Calculate the expected value of X?. c) Calculate the standard deviation of X. d) Calculate the expected value of Y = 4X + 5. e) Calculate the standard deviation of Y = 4X + 5.Let X and Y be random variables with the joint density function f(x,y)=x+y, if x,y element of [0,1], and f(x,y)=0,elsewhere. Find the expected value of the random variable Z = 10X+14Y.
- Find the expected value of the function g(x) = x, where x is a random variable de- fined by the density f, (x) =G olexp 1 u(x)exp %3D 2Find the expected value of the function g(X) = X' where X is a random variable defined by the density fx(x) = (1/2)u(x)e(-x/3). Select one: O a. 243 O b. none of these O c. 48 O d. 162 REDMI NOTE 9S AI QUAD CAMERAA random variable Y has a probability density function f(y) = A(y − 1.5) over the state space−2 ≤ y ≤ 3, where A is a constant. Calculate the median of the random variable Y.