The distribution of the amount of gravel (in tons) sold by a particular construction supply company in a given week is a continuous random variable X with pdf f(x) = 3/2 (1 – x2 )0 ≤ x ≤ 10                    0       otherwise i. Determine the cumulative distribution function (cdf) of X ii. Calculate the mean of X iii. Calculate the variance of X

A random variable X takes value 1 with probability and the value 2 with the remaining probability. What is the variance of X, Var[X]? O 1/3 3/4 2/3 1/2 O 1/4

A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels​ (in milligrams per deciliter of​ blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and​ dependent, and the population is normally distributed. At α=0.05​, can you conclude that the new cereal lowers total blood cholesterol​ levels? Patient 1 2 3 4 5 6 7   Total Blood Cholesterol (Before) 215 225 235 240 255 260 225   Total Blood Cholesterol​ (After) 214 222 240 237 254 257 222         Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative​ hypotheses, where μd=μ1−μ2. Choose the correct…

1. Let X be a random variable with pdf f(x) = 1,0 3).

The random variable X takes value O with probability, and value 1 with the remaining probability. The random variable Y takes value 100 with probability and value 101 with the remaining probability. What is the relation between the variance of X and the variance of Y? Var[X] Var[Y] "

Given pdf f (x) = 1.5x2  for −1< x < 1. Determine variance of X.

Suppose that y, is an independent response variable (i = 1.....n) with mean, such that g(i) = n₁ = X₁B, where g(.) is a link function, X, is a vector of covariates and 3 is a px 1 vector of coefficients. Let the variance of y; be Var (Y) = V(i), where V(.) is a known function and is a scale parameter. Given: Zi= g'(pi) (Yi - Pi) + Ni w₁ = [V (pi) (g'(pi))²]-¹ 8 where g'(μ) = 9(μ) (a) Show that E(Z₁) = X₂B (b) Show that Var (Z₁) = w¹o. (c) Estimate 3 by minimizing Σ, wi( E(Z₁))² with respect to 3. After you found 8, find the Var(8) and E(3). What do you conclude?

Consider the distribution of a discrete variable Y whose cumulative distribution function is given by 0, y < 12 12 ≤ y < 32 32 ≤ y ≤ 48 1, 48 ≤ y Enter below the variance of this distribution. F(y) 0.151, 0.699,