A random variable X has E(X²) = 20 and ux = 2. Find the standard deviation of X %3D (ox). O 4 18 O V18 O 16

EXER 6.3 Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete random variables, with joint PMF given by: SHOW SOLUTIONS X\Y 0 1 6 0 28 6 1 28 2 0 333333 28 28 28 2120 28 0

X is a random variable with mean  μ  and variance  σ2  . The standard form of X is Z =( X — μ)/σ  . What are the mean and variance respectively of Z

The mean and standard deviation of a random variable x are 0 and 4 respectively. Find the mean and standard deviation of the given random variables: (1) y = x+ 1 O = (2) v = 8x (3) w = 8x +1

Let X be a random variable with mean u= E(X) = 10.33 and variance o = 12.81. Determine: E{10- E 10- 4

Calculate the mean and standard deviation of the metabolic rates in Example 3.29 (page 116), showing each step in detail. First find the mean x by summing the 7 observations and dividing by 7. Then find each of the deviations xi − x and their squares. Check that the deviations have sum 0. Calculate the variance as an average of the squared deviations (remember to divide by n − 1). Finally, obtain s as the square root of the variance.

The mean and standard deviation of a random variable x are 4 and 1 respectively. Find the mean and standard deviation of the given random variables: (1) y=x+3 μ = 0 = (2) V μ = 0 = 2x (3) w 2x + 3 μ = 0 =

A random variable X follows a gamma distribution having a mean of 384 and a CoV of 0.316. What is the value of the PDF, fy(x), when x = 337?

A Gaussian random variable with variance 10 and mean 5 is transformed to Y=e. Find the pdf of Y.

Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day io patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: E(X)=0.4 and V(X)=0.384 O None of these O E(X)=0.5 and V(X)=0.475 O E(X)=0.3 and V(X)=0.291