Question

In: Math

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.

Expert Solution

Ley Y and Z be two independent observations from X~U(7,13)

SO,

, 7<x<13

Define, , 0<P<1

So,

pdf of P,

P ~ Uniform (0,1)

Thus,

independently

By Method of convolution, pdf of ,

if 1<t<2 ,

So,

if 0<t<1 ,

We have to find P(X+Y>25) :

milcah answered 1 month ago

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) =

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?

1. Suppose x is a random variable best described by a uniform probability distribution with and Find 2....

1. Suppose x is a random variable best described by a uniform probability distribution with and Find 2. Suppose x is a random variable best described by a uniform probability distribution with and Find 3. Suppose x is a random variable best described by a uniform probability distribution with and Find 4. Suppose x is a random variable best described by a uniform probability distribution with and Find 5. Suppose x is a random variable best described by a uniform probability distribution with and Find 6. Suppose x is a...

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.

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...

(a) If X is a uniform random variable with positive probability on the interval [0, n],...

(a) If X is a uniform random variable with positive probability on the interval [0, n], find the probability density function of eX (b) If X is a uniform random variable with positive probability on the interval [1, n], find E [1/X].

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 U be a continuous uniform variable over the interval [0, 1]. What is the probability...

Let U be a continuous uniform variable over the interval [0, 1]. What is the probability that U falls within kσ of its mean for k = 1, 2, 3?

2. Let X be a uniform random variable over the interval (0, 1). Let Y =...

2. Let X be a uniform random variable over the interval (0, 1). Let Y = X(1-X). a. Derive the pdf for Y . b. Check the pdf you found in (a) is a pdf. c. Use the pdf you found in (a) to find the mean of Y . d. Compute the mean of Y by using the distribution for X. e. Use the pdf of Y to evaluate P(|x-1/2|<1/8). You cannot use the pdf for X. f. Use...

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