X follows the log-normal distribution. If, P (X < x) = p1 and P (log X...
If the random variable x follows a normal distribution N(-3,1), then (a) P(x=2)= [a] (b) P(x>-3)=[b]
Two inner products are given on P? (z) as follows. If p(z) = Po + P1 z + P2 a? and q(z) = % +1 r+2 a are two elements of P? (x) then p(z) •1 q(x) = Po o + P1 91 + P2 2 and p(2) •2 q(x) = / p(=) • q(z) dz . Evaluate (2+ 2z – 3r) •2 (-4- 3z + 2z?) = (2+ 2x – 3z) • (-4– 3z + 2z?) = and %3!
Prove that each of the following conclusions (C) follows from the given premises. P1: (Ǝx)(P(x) ∧ (∀y)(B(y) ⇒ R(x,y))) P2: ~(Ǝx)(Ǝy)(P(x) ∧ F(y) ∧ R(x,y)) P3: (∀y) (F(y) ⇒ B(y)) C: ~(Ǝx)F(x)
A log-uniform probability distribution p(x) is one that makes the log of x uniformly distributed over some interval from x = a to x = b and is zero elsewhere. Determine p(x) in terms of a and b. Make sure it is normalized. Must derive what log is.
If the random variable x follows a normal distribution N(-3,1), then (a) P(x=2)= _______ (b) P(x>-3)= _______
iid Let X1,, X, ^ X~P for some unknown distribution P with continuous cdf F. Below we describe a ? test for the null and alternative hypotheses We divide the sample space into 5 disjoint subsets refered to as bins A1(-00,-2), A2 -(-2,-0.5), As -(-0.5,0.5), A4 (0.5,2) As -(2, oo). as functions of X, by Now, define discrete random variables For example, if Xi --0.1, then Xi є Аз and so Y;-3. In other words, Y, is the label of...
Problem 1. Let x be a random variable which approximately follows a normal distribution with mean i = 1000 and o = 200. Use the z-table (attached to this test), calculator, or computer software to find the following: Part A. Find P(> 1500). Part B. Find P(x < 900). Part C. Find P(900<x<1500).
Suppose that X follows a normal distribution with a mean of 850 and a standard deviation of 100. Find P(823<X<917).
Suppose the random variable X follows a normal distribution with mean µ = 84 and standard deviation σ = 20. Calculate each of the following: P(X > 100) P(80 < X < 144) P(124 < X < 160) P(X < 50) P(X > X*) = .0062. What is the value of X*?
Use the normal distribution to find a confidence interval for a difference in proportions p1-p2 given the relevant sample results. Assume the results come from random samples.A 95% confidence interval for p1-p2 given counts of 94 yes out of 200 sampled for Group 1 and 28 yes out 160 sampled for Group 2 Give the best estimate for p1-p2, the margin of error, and the confidence interval.give the best estimate,margin of error, and confidence interval Round your answers to three...