Consider the probability density function if x < -2 f(x) = {3 (8 + 2x –x²) if – 2 4. Find Var(X). Select one: 171 O O O
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- For the probability density function f(x) = 3x^2 on [0,1], find: V(X)Suppose the joint probability density of X and Y is fX,Y (x, y) = 3y 2 with 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 and zero everywhere else. 1. Compute E[X|Y = y]. 2. Compute E[X3 + X|X < .5]Verify that p(x) = 3x - 4 is a probability density function on [1, oo)and calculate its mean value.
- Verify that p(x) = 3x−4 is a probability density function on [1,∞) and calculate its mean value.Find a value of k that will make f a probability density function on the indicated interval.ƒ(x) = kx3; [2, 4]Determine k so thatf(x, y) = kx(x − y) for 0 < x < 1, −x < y < x0 elsewherecan serve as a joint probability density.
- The life (in years) of a laptop battery has a probability density function defined by P(x)=12e−x/2P(x)=12e-x/2for x in [0,∞)[0,∞). Find the probability that a randomly selected laptop battery will last between 3 and 8 years?Suppose that X and Y have the following joint probability density function.f (x, y) = 3x 400 0 < x < 6, y > 0, x − 4 < y < x + 4 (a) Find E(XY). (b) Find the covariance between X and Y.Consider the continuous probability density function defined by y= - 0.02x + 0.102 on -4.9 < x < 5.1 P(X > -0.9) = P(X < -0.9)
- Find the moment-generating function of the continuous random variable X whose probability density is given by f(x) = 1 for 0 < x < 1 0 elsewhere and use it to find μ’1,μ’2, and σ^2.If the probability density of X is given by f(x) =kx3(1 + 2x)6 for x > 00 elsewhere where k is an appropriate constant, find the probabilitydensity of the random variable Y = 2X 1 + 2X . Identify thedistribution of Y, and thus determine the value of k.If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?