please help me. Thanks in advance
please help me. Thanks in advance 7. Suppose the random variable U has uniform distribution on...
7. Suppose the random variable U has uniform distribution on [0,1]. Then a second random variable T is chosen to have uniform distribution on [O, U] Calculate P(T > 1/2)
7. Suppose the random variable U has uniform distribution on [0, 1]. Then a second random variable T is chosen to have uniform distribution on [0, U]. Calculate P(T> 1/2)
I. Let the random variable y have an uniform distribution with minimum value θ = 0 and maximum value θ2-1 and let the random variable U have the form aY +b, where a and b are both constants and a > 0. (a) Using the transformation method, find the probability density function for the random variable U when a 2 and b-4. What distribution does the random variable U have? (b) Using the transformation method, find the probability density function...
1. Suppose the random variable as a uniform distribution on [-k,k] a) Construct the pdf X. b) Calculate P(X > 2X > 1) in terms of 'k c) Calculate 'K if P(-2 < X < 2) =
2.5.9. The random variable X has a cumulative distribution function for xo , for xsO . for r>0 F(x) = z? 1 +x2 Find the probability density function of X.
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.)
Central limit theorem 9. Suppose that a random variable X has a continuous uniform distribution fx(3) = (1/2,4 <r <6 o elsewhere (a) Find the distribution of the sample mean of a random sample of size n = 40. (b) Calculate the probability that the sample mean is larger than 5.5.
Suppose that X is a continuous random variable whose probability density function is given by (C(4x sa f(x) - 0 otherwise a) What is the value of C? b) Find PX> 1)
Problem 7: 10 points Assume that a lifetime random variable (T) is exponentially distributed with the intensity λ > 0. I. Determine conditional density of the residual lifetime, T-u, given that T 〉 u. 2. Find conditional expectation, E TT>u
Q1. Assume that X is a continuous and nonnegative random variable with the cumulative distribution function F and density f. Let b>0. (a) Write the forinula for E(X b)+1. (b) Apply the general formula from (a) to exponential distribution with parameter λ > 0.