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7. Suppose the random variable U has uniform distribution on [0,1]. Then a second random variable...
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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).
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)
Assume U U(0,1), meaning that U is a continuous random variable, uniformly distributed in the interval (0, 1). Fix λ > 0 and define X =ナIn U. What is the density of X?
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) =
Let h be an exponentially-distributed random variable with the distribution function p- exp(-x) for x > 0 and ph = nction Ph 0 for a s 0. Derive the distribution function of its square root, Solution: 2y exp(-y2
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2.5.1. The probability function of a random variable Y is given by p (i)-% 1 0, 1, 2, , where λ is a known positive value and c is a constant. (a) Find c. (b) Find P(Y 0) (c) Find P(Y > 2).
1 point) Suppose a random variable x is best described by a uniform probability distribution with range 2 to 5. Find the value of a that makes the following probability statements true. (a) P(x <a) -0.18 a E (b) P(x < a) 0.78 (c) P(x 2 a) 0.23 (d) P(x > a) = 0.95 a= (e) P( 1.78 x a) = 0.02 a=
(5 pts) Let U be a random variable following a uniform distribution on the interval [0, 1]. Let X=2U + 1 Calculate analytically the variance of X. (HINT : Elg(z)- g(z)f(x)dr, and the pdf. 0 < z < 1 0 o.t.w. f(x) of a uniform distribution is f(x) =
4. Let y1θ ~iid Uniform (0,0), for i-1, n, Assume the prior distribution for θ to , be Pareto(a, b), where p()b1 for 0> a and 0 otherwise. Find the posterior distribution of θ.
Let U and V be independent Uniform[0, 1] random variables. (a) Calculate E(Uk) where k > 0 is some fixed constant (b) Calculate E(VU)