What is P(X > −1) if (a) X has a Uniform distribution on the interval (−2,...

What is P(X > −1) if (a) X has a Uniform distribution on the interval (−2, 2). (b) if X has a Normal distribution with µ = −2 and σ = 2.What is P(X > −1) if

(a) X has a Uniform distribution on the interval (−2, 2).

(b) if X has a Normal distribution with µ = −2 and σ = 2.

Expert Solution

a) X ~ U(-2 , 2)

P(X < x) = (x - (-2)) / (2 - (-2))

P(X > -1) = 1 - P(X < -1) = 1 - [(-1 - (-2)) / (2 - (-2))] = 1 - 1/4 = 0.75

b)

= P(Z > 0.5)

= 1 - P(Z < 0.5)

= 1 - 0.6915

= 0.3085

orchestra answered 2 years ago

The random variable X follows a CONTINUOUS UNIFORM DISTRIBUTION over the interval [50, 250]. Find P(80...

The random variable X follows a CONTINUOUS UNIFORM DISTRIBUTION over the interval [50, 250]. Find P(80 < X < 135). P(80 < X < 135) =

Let X have a uniform distribution on the interval [A, B]. (a) Obtain an expression for...

Let X have a uniform distribution on the interval [A, B]. (a) Obtain an expression for the (100p)th percentile, x. x = (b) Compute E(X), V(X), and σX. E(X) = V(X) = σX = (c) For n, a positive integer, compute E(Xn). E(Xn) =

A random variable X follows a uniform distribution on the interval from 0 to 20. This...

A random variable X follows a uniform distribution on the interval from 0 to 20. This distribution has a mean of 10 and a standard deviation of 5.27. We take a random sample of 50 individuals from this distribution. What is the approximate probability that the sample mean is less than 9.5

Let X have a uniform distribution on the interval (7, 13). Find the probability that the...

Let X have a uniform distribution on the interval (7, 13). Find the probability that the sum of 2 independent observations of X is greater than 25.

A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1,...

A geometric distribution has a pdf given by P(X=x) = p(1-p)^x, where x = 0, 1, 2, ..., and 0 < p < 1. This form of the geometric starts at x = 0, not at x = 1. Given are the following properties: E(X) = (1-p)/p, and Var(X) = (1-p)/p^2 A random sample of size n is drawn; the data are X1, X2, ..., Xn. A. Derive the Fisher information function for the parameter p. B. Find the Cramér-Rao...

1. Let X be the uniform distribution on [-1, 1] and let Y be the uniform...

1. Let X be the uniform distribution on [-1, 1] and let Y be the uniform distribution on [-2,2]. a) what are the p.d.f.s of X and Y resp.? b) compute the means of X, Y. Can you use symmetry? c) compute the variance. Which variance is higher?

If X has a binomial distribution with p = 0.5, then the distribution of X is...

If X has a binomial distribution with p = 0.5, then the distribution of X is _______. a)left-skewed b)uniform c)right-skewed d)symmetric

2. Let X1, ..., Xn be a random sample from a uniform distribution on the interval...

2. Let X1, ..., Xn be a random sample from a uniform distribution on the interval (0, θ) where θ > 0 is a parameter. The prior distribution of the parameter has the pdf f(t) = βαβ/t^(β−1) for α < t < ∞ and zero elsewhere, where α > 0, β > 0. Find the Bayes estimator for θ. Describe the usefulness and the importance of Bayesian estimation. We are assuming that theta = t, but we are unsure if...

Suppose X has probability distribution x: 0 1 2 3 4 P(X = x) 0.2 0.1...

Suppose X has probability distribution x: 0 1 2 3 4 P(X = x) 0.2 0.1 0.2 0.2 0.3 Find the following probabilities: a. P(X < 2) b. P(X ≤ 2 and X < 4) c. P(X ≤ 2 and X ≥ 1) d. P(X = 1 or X ≤ 3) e. P(X = 2 given X ≤ 2)

Let X be a continuous random variable that has a uniform distribution between 0 and 2...

Let X be a continuous random variable that has a uniform distribution between 0 and 2 and let the cumulative distribution function F(x) = 0.5x if x is between 0 and 2 and let F(x) = 0 if x is not between 0 and 2. Compute 1. the probability that X is between 1.4 and 1.8 2. the probability that X is less than 1.2 3. the probability that X is more than 0.8 4. the expected value of X...

Question