Exercise: Variance of the uniform Suppose that the random variable X takes values in the set...

Exercise: Variance of the uniform

Suppose that the random variable X takes values in the set {0,2,4,6,…,2n} (the even integers between 0 and 2n, inclusive), with each value having the same probability. What is the variance of X? Hint: Consider the random variable Y=X/2 and recall that the variance of a uniform random variable on the set {0,1,…,n} is equal to n(n+2)/12.

Var(X)=

Expert Solution

TOPIC:Discrete uniform distribution.

orchestra answered 2 years ago

a)Suppose random variable X has variance 1, Y has variance 4 and the variance of X...

a)Suppose random variable X has variance 1, Y has variance 4 and the variance of X + Y is 6. Which one of the statements below is correct? Group of answer choices Random variables X and Y are positively correlated Random variables X and Y are not correlated Random variables X and Y are negatively correlated Random variables X and Y are independent b)Suppose random variable X has variance 4, Y has variance 1 and the variance of X +...

(a) Let X be a continuous random variable which only takes on positive values on the...

(a) Let X be a continuous random variable which only takes on positive values on the interval [1, 4]. If P(X) = (√ x + √ 1 x )C 2 for all x in this interval, compute the value of C. (b) Let X be a random variable with normal distribution. Let z represent the z-score for X, and let a be a positive number. Prove that P(z < |a|) = P(z < a) + P(z > −a) − 1.

Consider the two dependent discrete random variables X and Y . The variable X takes values...

Consider the two dependent discrete random variables X and Y . The variable X takes values in {−1, 1} while Y takes values in {1, 2, 3}. We observe that P(Y =1|X=−1)=1/6 P(Y =2|X=−1)=1/2 P(Y =1|X=1)=1/2 P(Y =2|X=1)=1/4 P(X = 1) = 2/ 5 (a) Find the marginal probability mass function (pmf) of Y . (b) Sketch the cumulative distribution function (cdf) of Y . (c) Compute the expected value E(Y ) of Y . (d) Compute the conditional expectation...

A multivariate random variable (X1, X2, X3) takes values in the following set S with equal...

A multivariate random variable (X1, X2, X3) takes values in the following set S with equal probability: S = {(1, 1, 1),(3, 0, 0),(0, 3, 0),(0, 0, 3),(1, 2, 3)}. a) Compute E[X1|X2 = i], for each i = 0, 1, 2, 3, and E[X1]. b) Compute the marginal p.m.f. of Xi for each i = 1, 2, 3.

Suppose X is a uniform random variable on the interval (0, 1). Find the range and...

Suppose X is a uniform random variable on the interval (0, 1). Find the range and the distribution and density functions of Y = Xn for n ≥ 2.

Data set : Data Set G: Assume the population values are normally distributed. Random variable: x...

Data set : Data Set G: Assume the population values are normally distributed. Random variable: x = weight of border collie in pounds sample size = 25 34.1 40.8 36.0 34.9 35.6 43.4 35.4 29.3 33.3 37.8 35.8 37.4 39.0 38.6 33.9 36.5 37.2 37.6 37.3 37.7 34.9 33.2 36.2 33.5 36.9 1. Choose another confidence level similar to one found in the homework (do not use the confidence level from the posted example). Based on the second confidence level,...

X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent...

X is an independent standard uniform random variable X ∼ Uniform(0, 1) Y is an independent standard uniform random variable Y ∼ Uniform(0, 1) U = min(X, Y ) V = max(X, Y ) Find the correlation coefficient of V and U , ρ(U, V) = Correlation(U, V).

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...

Random variable X is a continuous uniform (0,4) random variable and Y=X^(1/2). (Note: Y is always...

Random variable X is a continuous uniform (0,4) random variable and Y=X^(1/2). (Note: Y is always the positive root.) What is the P[X>=E[X]] ? What is the E[Y] ? what is the P[Y>=E[Y]]? what is the PFD of fY(y)?

Suppose X is a discrete random variable with mean μ and variance σ^2. Let Y =...

Suppose X is a discrete random variable with mean μ and variance σ^2. Let Y = X + 1. (a) Derive E(Y ). (b) Derive V ar(Y ).

Question