Non-probability sampling:

a. includes stratified sampling.

b. denies the researcher the use of statistical theory to estimate the probability of correct inferences.

c. always produces samples that possess distorted characteristics relative to the population.

d. is always less desirable than probability sampling.

e. requires the manipulation of sampling frames.

(10) 4. Answer the following: (5) a) Differentiate between descriptive and inferential statistics with an example for each. (5) b ) State the Central Limit Theorem (CLT). The formal statement is the most important theorem of probability and concept of statistical inference. Why? Explain your answer using graphs to illustrate your point.Problem 8 Trc) A silicon wafer is doped by Phosphorous via Diffusion at 1090C. 12:00 1000 Assume the measured Phosphorous profile can be represented by a Cu Gaussian function. The solid solubility of phosphorous is 1017 cm", 10 and the measured junction depth is 1 um at a substrate LI concentration of 1016 cm 3. Calculate the diffusion time and the total Au Na dopant in the diffused layer. H Slope for E, = 0 I EV 2 ev 3 ev Difinaion coefficient D jom-Al S ev C In 0.6 U.T LOOUT (K-)1. Orthogonally diagonalize the following matrices, if possible. If it is possi- ble, give the spectral decomposition of the matrix. (a) 2 to (b) 2 to 0 1 2 09 - K (c) 0 3 0 2. Use the spectral decomposition (in reverse) to find the matrix A such that (1, -1, 1) is an eigenvector with eigenvalue 2, and (2,3, 1) and (4, -1, 5) are eigenvectors with eigenvalue -3.A probability distribution which can take any value on the real line (-0o, co). Has two parameters: mean (u) and standard deviation When u = 0 and 6 = 1, called the standard normal distribution. Extra credit: what is probability of a normally distributed random variable taking on a specific value, say 0? Probability and Statistical Inference