If the probability density function of the ran lom varinble X is (1- p)-'p if z = 1,2,3, 4,., 00 S(r) = otherwise,
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Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X² – 10X +…
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Q: Let (X; Y) be a continuous random vector with joint probability density function 0.5 -1sx 0) equals
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Q: Suppose that X is a normal random variable with parameters u = 5 and o = 1. Define Y = X2 – 10X +…
A: 1] X is a normal random variable 2] μ=5 and σ=1 3] Y=X2-10X+25
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- Suppose that X and Y are independent and uniformly distributed random variables. Range for X is (−1, 1) and for Y is (0, 1). Define a new random variable U = XY, then find the probability density function of this new random variable.Calculate the probability that X + Y ≤ 2 for random variables withjoint probability density function as in .Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?
- A random variable X has a Pareto distribution if andonly if its probability density is given by f(x) =⎧⎪⎨⎪⎩αxα+1 for x > 10 elsewhere where α > 0. Show that μ r exists only if r < α.Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: f(x) = 1/10. a) According to Chebychef’s rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. P(|x − µ| <2 ∗ σ) b) What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?Let the random variable X follow a gamma distribution with α = 4 and β = 4. If Y = X2 what is the density function of Y?
- The random variable x is known to be uniformly distributed between 1.0 and 1.5.a. Show the graph of the probability density functionSuppose that two-dimensional continuous random variable (X, Y) has joint probability density function given by f(x,y) = 24xy, x is less than equal to 1 and greater than equal to 0, y is less than equal to 1 and greater than equal to 0, x+y is less than equal to 1 and greater than equal to 0. Check that E(Y) = E[E(Y|X)] and V(Y) = E[V(Y|X)] + V[E(Y|X)].Let X be a random variable that indicates the charging time of a battery. The probability density function is as in the picture. If the battery is known to charge in more than 2 hours, the probability that it will be less than 4 hours?
- A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint probability density function given by f(x,y)={(3/2)(x2+y2) 0<x<1 and 0<y<1 0 otherwise What is the probability that both machines are in operation for more than half an hour? (Round the final answer to four decimal places.)Suppose the random variables X and Y have joint probability density function f(x,y) given by: (image)Find: P(X < Y) = fX|Y=y (x)Suppose that the probability density function of the length of computer cables is f (x) = 2x/(32) for x between 0 and 3 meters. Determine the mean of the cable length. Please enter the answer to 2 decimal places.