Problem 5. A particle of mass 1g has a random velocity X that is uniformly distributed...
Problem #9: The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 125 x 2-5x x >0. The kinetic energy of the particle is Y - X?. Suppose that the mass of the particle is 36 yg. Find the probability distribution of Y. (Do not convert any units.)
The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 27 x2 -3x x >0. The kinetic energy of the particle is Y = {mXSuppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.)
Let X be a uniformly distributed continuous random variable that lies between 1 and 10. i. Sketch the probability density function for X. ii. Find the formula for the cumulative distribution for X and use it to compute the probability that X is less than 6
The velocity of a particle in a gas is a random variable X with probability distribution fX (x) = 256 x^2 e^(−8x) x > 0. The kinetic energy of the particle is Y = (1/2 )* (mX^ 2). Suppose that the mass of the particle is 49 yg. Find the probability distribution of Y. (Do not convert any units.)
Problem #3: The velocity of a particle in a gas is a random variable X with probability distribution fx (x) = 343 z2 e-7x x>0. The kinetic energy of the particle is Y = 2 mx2. Suppose that the mass of the particle is 16 yg. Find the probability distribution of Y. (Do not convert any units.) Enter your answer as a symbolic 343/16*sqrt(2*y/16)*(e^(-7*sqrt(2*) function of y, as in these examples Problem #3: 343 V (e-71 (20)/16) + e7V (2/16))...
The velocity of a particle in a gas is a random variable X with probability distribution fx(x) = 27x2e-3x x >0. The kinetic energy of the particle is Y = mx?. Suppose that the mass of the particle is 64 yg. Find the probability distribution of Y. (Do not convert any units.)
A random variable X is uniformly distributed on the interval [-TT/2.TT/2]. X is transformed to the new random variable Y = T(X) = 2 tan(X). Find the probability density function of Y. (Hint: (tan x)' = 1/cos2x, cos?(tan 1x) = 1/(1+x2)
If X is uniformly distributed over (-2, 1], find (i) the cumulative distribution function of Y1 = |X| (ii) Find the probability density function of Y2=e^2X
2. Suppose ten particles, each of mass 2 grams, are moving independently, each with a velocity (cm/sec) which is normally distributed with mean 0 and variance 9. Find the distribution of the total kinetic energy of all of these particles. (the kinetic energy of a particle of a mass m 13 point] grams travelling at a velocity v cm/sec is given by mu2 ergs.)
Problem 9: 10 points Suppose that X, Y are two independent identically distributed random variables with the density function f(x)= λ exp (-Az), for >0. Consider T- and find its cumulative distribution function and density function.